This paper presents a novel method for tomographic measurement and data analysis based on crowdsourcing. X-ray radiography imaging was initially applied to determine silo flow parameters. We used traced particles immersed in the bulk to investigate gravitational silo flow. The reconstructed images were not perfect, due to inhomogeneous silo filling and nonlinear attenuation of the X-rays on the way to the detector. Automatic processing of such data is not feasible. Therefore, we used crowdsourcing for human-driven annotation of the trace particles. As we aimed to extract meaningful flow parameters, we developed a modified crowdsourcing annotation method, focusing on selected important areas of the silo pictures only. We call this method “targeted crowdsourcing”, and it enables more efficient crowd work, as it is focused on the most important areas of the image that allow determination of the flow parameters. The results show that it is possible to analyze volumetric material structure movement based on 2D radiography data showing the location and movement of tiny metal trace particles. A quantitative description of the flow obtained from the horizontal and vertical velocity components was derived for different parts of the model silo volume. Targeting the attention of crowd workers towards either a specific zone or a particular particle speeds up the pre-processing stage while preserving the same quality of the output, quantified by important flow parameters. However, due to their complexity or uniqueness, the difficulty of achieving sufficiently high accuracy, or simply economic factors, different methods of processing such datasets are preferred, based on human orientation. Examples of such tasks, including projects pertaining to image processing, have been reported in the literature [Crowdsourcing is an emerging method for processing large amounts of data using geographically-distributed heterogeneous workers. This method has proven suitable for resolving computational problems that are difficult to solve automatically, as it is capable of coupling the data processing capabilities of automated systems with human intelligence. Another advantage of crowdsourcing is the reduced cost . Most of the tasks submitted to widely-available crowdsourcing servers  tasks is a common part of crowdsourcing methods and is possible using most popular platforms ,7. HowevCrowdsourcing systems coordinate the efforts of distributed workers and synthesize the results to solve problems that a single individual could not achieve on the same scale, within the same budget or time-frame. This approach makes it possible to complete problems at a level of complexity beyond the capabilities of the research personnel available. Usually, a few minutes of online training in the form of a video or illustrated manual is sufficient for a new worker to begin the task. This is important from the point of view of this research, since neither machine learning algorithms nor standard image processing methods can currently perform efficiently in the application presented here, as reported in ,11. On tCrowdsourcing tasks can be efficiently tailored to a range of problems relating to process tomography sensing, especially for reconstructed images. There have been previous reports of the successful application of the general method to annotate X-ray radiography data using non-expert workers . This paThe main contribution of this paper is to evaluate the approach on the basis of industrial tomographic measurement data, which was impossible to process automatically using currently-available approaches, in order to provide a meaningful quantitative description of the flow in terms of parameters. An additional contribution of this paper is the proposed method of a targeted crowdsourcing, in which each contributor is given a narrowed down task in comparison to the usual full-frame work assignment. This involved identifying the position of a single marker or a set of markers in a small, selected area of the images in a sequence of assigned frames. Such targeting of the workers’ attention aims to reduce the effort required from any single participant, whilst providing data of comparable or superior accuracy to datasets processed using classical crowdsourcing systems.The rest of the paper is organized as follows. This section introduces the two key elements of the research background, namely industrial tomography for process monitoring and the basics of the gravitational flow of bulk solids.In the context of industrial processes, tomography is closely associated with imaging, since images provide rich information concerning the monitored process ,16,17. OX-ray tomography provides much higher spatial resolution than electrical process tomography, making it more convenient and reliable as a tool for investigating processes. However, detailed imaging in 3D requires a substantial number of projections around the scanned body. Guillard et al.  presentsThe gravitational flow of solid particles is relevant to a number of industrial processes, in which bulk solids are stored in silos. Such granular material may be of natural provenance  or be generated in the process of extraction , as well as being deliberately processed . The storage of bulk material, whilst seemingly very simple, is actually a complex process requiring sophisticated analysis. The quality of material storage, as well as the ease, efficiency, and safety of unloading strongly depend on the method by which the silo is filled . The iniSystems for measuring the process of handling granular materials and measuring the levels of silos are well established. Since the early 1960s, studies focused mainly on predicting the type of flow  and its changes , analyziIn recent years, Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV) have been used extensively to measure the translational velocity field of granular assemblies . VariousIn order to investigate the two types of silo flow using an industrial X-ray tomography setup, a dedicated model of a silo was constructed. The rectangular silo model had 5 mm-thick walls made of perspex sheets, 340 mm in height, with an inner size of Trace particles  with relatively neutral buoyancy were mixed with a granular material (sand) before the experiments . InitialOne notable drawback of the applied imaging technique, however, lies in the flatness of the generated image. Some features of the observed process may have been concealed by objects closer to the emitter. Due to this “shadowing” effect, some of the objects may be partially visible  or totally invisible in certain random individual or consecutive frames. Such behavior must be taken into consideration in the subsequent analysis, as it causes issues for automatic processing of trace particle images using both classical image processing algorithms and modern approaches such as neural network-based methods .Radiography images were taken of funnel flow in the cases of dense and loose initial packing densities. The flow area in each case was different, since for initially dense packing, the funnel should be narrower than in the case of loose packing. In addition, the contrast between the funnel zone and the remainder of the material in the radiography images was much higher in the case of dense flow. The combination of inherent graininess at such scales and the grainy nature of the observed material itself probably makes extraction of the relevant features in the image an insurmountable task for classical image processing methods. However, as previously shown  and obseDownward velocity was calculated based on the positions of particles provided by the crowdsourcing system (details on the crowd workflow are given later in this paper). In order to compare the velocity for different heights above the silo outlet, the area of the silo was divided into nine sections. This division was established based on expert knowledge of the gravitational flow process, with each zone containing part of the funnel flow. Three crowdsourcing data processing methods were applied. The first method was an established classical procedure , according to which each worker processed all the particles visible in the picture on each image in the assigned sequence. The second was a zone-particle tracking method, whereby each worker focused on and processed a limited number of trace particles located only within a single zone of each image in the assigned sequence. For this method (the “zone-targeted” method), we used the same zone grid as for the comparison of flow velocity, as shown on the left in The first, classical method was an implementation of the well-known crowdsourcing paradigm, while the other two  were novel and are evaluated within this study. Both require an additional initialization step, which involved preparing (marking) the first frame of the assigned image sequence in order to indicate the zone of interest (for the targeted zone method) or either selecting the starting particle or giving instructions on how to select the particle of interest (for the single-particle-targeted method).The general workflow for processing the X-ray trace particle images is presented in Option (#1) was a typically mundane task. The volumetric parameters of the flow were the required output. Suppose there were 1000+ images in sequence, showing up with 50 tracking particles. At least those in the center  needed to be analyzed in each picture. The analysis consisted of tracing the movement of the particles in consecutive frames. Heterogeneous damping of radiation resulted in non-uniform representation of the tracing particles on adjacent images, which created difficulties for automatic image processing algorithms to detect them efficiently, as described previously in Option (#2) involved uploading selected datasets to a crowdsourcing system for distribution among workers. Different strategies for dividing, managing, and verifying the results are used in commercial crowdsourcing systems. However, a simple approach was used in this work . The tasWhen the worker finished with a single frame, the marked particles were saved and the markings transferred to the next picture in the sequence. In the next picture, the worker could adjust the positions of the markings indicating the particles, since generally there were only slight shifts between the particles on consecutive images as the bulk flow proceeded. The markings from the previous frames were reported to be helpful, as the trace particles may not be equally exposed on consecutive images . WorkersWe used three different approaches , as described in The output of the crowdsourcing system was two-fold. Firstly, it exported images with the tracked particles marked (annotated) on each frame. The aggregated trajectories of the particles may also be marked. Secondly, numerical data conveying the exact positions of each particle in each frame were exported from the system. There are different approaches to the process of annotating the images. The usual way is to mark the region of interest with a circle of a specific, highly-contrasting color, or to place a marker at the approximate center of the region . Some otThe first goal of this work was to test crowdsourcing as a valid method for analyzing experimental radiography data, supporting the determination of meaningful process parameters. Therefore, a quantitative scenario for calculating the velocity of each marked particle based on the position extracted from the system output was designed. A pilot study was conducted with two domain experts and up to ly dense , as wellly dense  packing As anticipated, the higher overall velocity was observed in the center zones of each row  than in the side zones . The highest velocity was observed at the bottom of the hopper component of the silo: Zone H ,49. The The results presented here were for the single-particle method, but the accuracy and precision calculated for all three methods were satisfactory and did not differ significantly. First of all, we considered accuracy compared to the ground truth baseline prepared by two experts. All the methods achieved comparable results, with variations of no more than 2%. Precision taken as the repeatability of results also reached 98%. Next, we examined the duration, i.e., the length of time required to complete the task by workers using different methods.By quantitative analysis of radiographic images with the aid of the crowdsourcing system, it is possible to obtain a profile of the granular material velocity during the silo discharging process. The results provided additional knowledge about granular flows, making detailed comparative analysis of flow dynamics possible. Such analysis can be conducted on the basis of the calculated velocity profile derived from X-ray imaging data. The results obtained in our study are in agreement with previously-reported data ,49.The proposed crowdsourcing system enabled the distribution of the imaging data (image sequences) for different flow fragments  tests. The participants completed a self-assessment rubric, in which they evaluated six main factors related to the given tasks, namely mental, physical, and temporal demand, how they perceived their performance in terms of quality and effort, and finally, the level of frustration induced by the task. These factors approximated to some extent the measurement of task complexity, the user experience, and the usability of the proposed approach, all in relation to the background of individual workers.Diagrams of the TLX results are presented in The NASA TLX index tests showed a significant decrease in mental and temporal demand, as well as a drop in job frustration for both conditions (dense and loose silo filling), for both proposed methods compared to the classical crowdsourcing method. The results were better (a larger drop) for the single-particle tracking method than for the zone-tracking targeted method. However, the decrease in physical demand was slightly more prominent for the single-particle method and was significant for both methods only in the case of the loose filling condition. A different effect can be observed in the category of effort. Effort was reported to decrease significantly, mainly for the single-particle method (a drop of more than 50%) compared to the classical baseline method. Performance went up significantly, by more than 10%, but only for the single-particle method. Interestingly, performance increased by more than 10% only for the single-particle method. Performance was not perceived to be significantly different for the zone-tracking method, no matter the condition, yet it was perceived to be worse than the classical method in the case of dense filling.The methodology presented here provides a practical way to analyze reconstructed images, when automatic methods for feature extraction using classical computer vision algorithms are not efficient. The proposed method based on crowdsourcing was verified using real measurement data, and the results were in agreement with those obtained by other research methods. Specifically, the velocity vectors calculated using the crowdsource-annotated data were verified. The positions of trace particles were annotated in sequences of radiography data over time and were used to determine velocity vectors in three different parts of a silo container during bulk solid flow. In this paper, we showed a method for how to determine the flow velocity based on horizontal and vertical velocity components of trace particles.In our comparison of three approaches to crowdsourcing the processing of image sequences, the proposed zone-targeted and single-particle targeted methods performed well, giving task completion time benefits. Further investigation is needed to prove the usefulness of the methodology for other applications.Our results showed definite potential for further applications of the targeted crowdsourcing methods. Methods that decrease overall workload are needed to reduce common limitations of crowdsourcing, such as sloppiness and the low percentage of quality results ,14. MoreIn this work, we presented a method for extracting process parameters using crowdsourcing. The proposed data processing workflow was applied to study gravitational silo flow, measured by X-ray radiography, and proved to be a reliable and useful way to process tomography data. Crowdsourcing proved to be efficient for pre-processing raw images captured by an industrial standard 2D X-ray radiography sensor. The aggregated average output from the crowdsourcing system can be taken as the input for further, automatic or semi-automatic calculations, as demonstrated here in the case of calculations of the axial velocity of trace particles moving along a silo during unloading. An additional benefit of the proposed targeted crowdsourcing method is that it minimizes the cognitive workload, enabling similar research tasks to be completed more efficiently.


This paper presents two methods to optimize LoRa (Low-Power Long-Range) devices so that implementing multiplier-less pulse shaping filters is more economical. Basic chirp waveforms can be generated more efficiently using the method of chirp segmentation so that only a quarter of the samples needs to be stored in the ROM. Quantization can also be applied to the basic chirp samples in order to reduce the number of unique input values to the filter, which in turn reduces the size of the lookup table for multiplier-less filter implementation. Various tests were performed on a simulated LoRa system in order to evaluate the impact of the quantization error on the system performance. By examining the occupied bandwidth, fast Fourier transform used for symbol demodulation, and bit-error rates, it is shown that even performing a high level of quantization does not cause significant performance degradation. Therefore, the memory requirements of LoRa devices can be significantly reduced by using the methods of chirp segmentation and quantization so as to improve the feasibility of implementing multiplier-less filters in LoRa devices. The LoRa (Low-Power Long-Range) modulation technique is an excellent solution for many internet-of-things (IoT) applications due to its excellent energy consumption, link robustness and long-range capabilities at the expense of low bit rates ,2. LoRa M is the modulation order [The behavior of a LoRa chirp is controlled by both the spreading factor,  500 kHz ,5. Each duration . The traAs the demand for long-range, low-power IoT devices increases, so does the need to improve the spectral efficiency of these devices’ transmission. One promising solution is to implement a set of pulse shaping and matched square-root raised cosine (SRRC) filters in LoRa transmitters and receivers, respectively. The use of these filters can significantly reduce the bandwidth containing 99% of the total mean signal power while also reducing the out-of-band emissions created by LoRa devices ,7,8. TheThe challenge is that since LoRa devices are characterized by their low complexity, it is more difficult to justify the added resources required for filtering, especially when longer filters are required (which is often the case for LoRa devices with lower bandwidth settings ). Since Replacing hardware multipliers in a pulse-shaping filter can be done with a look-up table (LUT), provided there is a finite number of input sample values to the filter that are known. Instead of multiplying each incoming sample by a filter coefficient using a hardware multiplier, the result of every possible multiplication can be precalculated and stored in the LUT. Then, the LUT can output the correct product of the required multiplication based on the associated input sample value. The size of the LUT depends on both the number of unique input sample values and the filter length. In such an implementation, the complexity of the filter is measured by the cost of the memory instead of hardware multipliers.M possible input values for each chirp waveform. Furthermore, implementing multiple The problem with LoRa is that since discrete-time LoRa chirps are made up of In this paper, two methods of optimizing LoRa transmitters are proposed in order to reduce the complexity of filtering. First, waveform segmentation is used to generate an entire basic LoRa chirp waveform from only a portion of the total number of chirp samples in order to reduce the size of the chirp generation ROM. While this does not directly impact the LUT size, it reduces the overall memory requirement. This method is inspired by the CSS transceiver design presented in  and it hThe second method involves quantizing the LoRa chirp samples to a significant degree so as to reduce the number of unique input values to the multiplier-less filter, which helps to reduce the LUT size. While chirp segmentation does not add any error, quantization adds some rounding errors to the quantized chirp signals. It is important to ensure that the desired sample reduction can be achieved without significant performance degradation.The feasibility of implementing a multiplier-less SRRC pulse shaping filter in a LoRa transmitter will be evaluated in terms of the tradeoff between the potential sample reduction and impact of quantization noise on the performance. In order to quantify the effectiveness of the sample reduction, the number of samples required to form LoRa chirp waveforms and subsequent filtered signals shall be compared to that of an unoptimized LoRa device. The degree of sample reduction, therefore, depends on which spreading factors are supported, the length of the pulse shaping filter, if chirp segmentation is used, and the quantization step size (if any).Finally, the performance of the system will be evaluated for LoRa signals with various degrees of quantization. A LoRa communication system is simulated in Matlab, and the performance is evaluated in terms of the occupied bandwidth (OBW) of transmitted LoRa signals, the output of the fast Fourier transform (FFT) performed for symbol demodulation, and the bit-error-rate (BER). The goal is to find appropriate levels of quantization in order to significantly reduce the overall memory requirement while maintaining excellent performance.Basic LoRa chirp waveforms are used as the basis for the LoRa modulation technique. They are used in both the preamble and payload of transmitted LoRa packets. The expression for a continuous-time basic LoRa chirp waveform is shown in , where Tentation . The expm, as shown in xm[nFurthermore, in order to maintain the phase continuity between subsequent chirps, each modulated chirp waveform obtained from  is multid chirps ,6. PerfoWhile performing the complex multiplication will not affect the number of samples required for chirp generation, it will drastically affect the number of unique filter inputs. However, as in the case of basic chirp samples, it turns out that many phase-corrected sample values are shared among multiple In terms of implementation, the real and imaginary components are considered separately as they correspond to the I and Q channels in a practical system. However, since the magnitude of With that in mind, the following subsections detail the proposed methods and the resulting sample reduction compared to a standard LoRa device. It is also important to note that while basic chirp samples obtained from (2) are used for chirp generation, the LUT must account for each possible phase-corrected modulated chirp sample obtained from .It is perhaps more intuitive to begin by examining the inherent symmetry in the sequence of k is an integer representing the segment number. More importantly, each of these segments contains identical sample values, but they differ with predictable patterns of opposing signs and/or sample order. While it may not be obvious from rding to  and (6),k into (Using  with (2)shown in . Substit , reIn order to quantify the impact of chirp segmentation on the complexity of a practical system, the actual number of real and imaginary samples contained in the ROM and LUT must be considered. Let given by  for eachThe number of samples required in the filter LUT depends on both the number of filter coefficients  in order to exactly represent the theoretical response. If the quantization step size is increased, it is possible to reduce the number of unique filter input values in order to accommodate the use of longer filters. This is discussed further in the next section.B represent the number of fraction bits used for the system such that the uniform quantization step size is In order to implement a practical LoRa system, some level of quantization is necessary to represent the LoRa chirp signals. Since the chirp sample values are normally between B. B, namely 2, 4, 6, 8, and 10 bits.Assuming the use of chirp segmentation, the values of Once again, the total number of samples required to implement the LoRa transmitter for each quantization factor can be found from . The calBy comparing the results in The performance of different LoRa communication systems with additive white Gaussian noise (AWGN) channels was evaluated in Matlab. The pulse shaping and matched SRRC filters both have an upsampling/downsampling factor of The occupied bandwidth measurements were taken on a Keysight N9030A Spectrum Analyzer  using th Devices . The ANS Devices  in orderEach set of transmitted signals consists of 10 preamble symbols and 250 modulated chirp symbols. The signals were generated in Matlab and then sent to a Keysight N5182B Signal Generator . The cenThe LoRa spreading factor was set to 10, while the specified bandwidth was set to 125, 250, and 500 kHz. The measured OBW results can be found in Additionally, consider sample screenshots taken from the spectrum analyzer shown in m [M-point FFT and detecting which frequency bin contains the maximum energy. The index of the detected frequency bin is the LoRa symbol value.As illustrated in value, m ,6. The fM-point FFTs and spectrograms associated with quantized and non-quantized LoRa signals. Each tested LoRa signal corresponds to a symbol value of Since decoding the proper symbol value depends on accurate peak detection, it is important to ensure that the peak associated with the symbol value is clearly distinguishable from that of the quantization noise. While there is a clear increase in the noise level when the quantization step size increases, the desired FFT peaks, and frequency ramps remain clearly visible for each case. Even with only 2-bit fractional precision, the quantization noise is well over 20 dB below the peak of the desired frequency bin. Furthermore, the spectrograms for the cases where The BER tests were performed for filtered LoRa signals with and without quantization to see how they would perform under the effects of noise in an AWGN channel. The bandwidth was set to a fixed value of 125 kHz, while the spreading factor was varied from 6 to 12 for all tests. The BER results for each case are shown in The results for the non-quantized case can be corroborated by the simulated BER measurements of typical LoRa systems given in both ,14. It iTwo methods were presented to reduce the complexity of implementing multiplier-less SRRC pulse shaping filters in LoRa transmitters. These methods focus on reducing the required number of samples in the ROM used to generate basic chirp signals, as well as those required for the multiplier-less filter LUT. Chirp segmentation can be used to generate the entire basic LoRa chirp waveform from only a quarter of its samples without adding any additional error to the signal. Quantization can also be used to exponentially decrease the number of unique samples at the input to the multiplier-less pulse shaping filter at the cost of introducing small errors to the transmitted signal.Using both methods allows for a reduction in the number of stored samples so as to not only match, but also improve upon the results obtained from a standard LoRa device that does not contain a multiplier-less filter. For example, a system using 10-bit fractional precision and a length-17 multiplier-less pulse shaping filter requires fewer samples to be stored in memory compared to a standard LoRa system when supporting spreading factors 6 to 12. Even a device with a length-81 filter requires fewer stored samples than a standard device by quantizing the LoRa chirp samples to 8 fractional bits.Furthermore, it was shown that moderate levels of quantization do not hinder the decoding performance of LoRa devices, even under harsh channel conditions. Therefore, the quantization factor can be chosen based on the complexity requirements of the system. For example, devices intended for long-range communication require larger spreading factors and, as a result, a higher quantization factor to compensate for the added complexity. In conclusion, using the proposed sample reduction methods can aid in further alleviating the complexity concerns associated with implementing SRRC filters in LoRa devices.


This paper focuses on an improved imaging algorithm for spotlight synthetic aperture radar (SAR) with continuous Pulse Repetition Interval (PRI) variation in extremely high-resolution. Conventional SAR systems are limited in that a wide swath cannot be achieved with a high azimuth resolution in the meantime. This limitation can be overcome by Pulse Repetition Frequency (PRF) variation in a SAR system. However, there are problems such as the ambiguities of point targets or extended targets caused by nonuniform sampling. A reconstructive method, Nonuniform Discrete Fourier Transform (NUDFT) has been presented in the current literature, but it is rather computationally expensive. In this paper, a modified sinc interpolation based on NUDFT is proposed, which is used to reconstruct the uniformly sampled echo in time domain. Since the interpolation kernel length is relatively short, it is more computationally efficient. Then, the two-step processing approach combined with the modified sinc interpolation is further presented, which has much better accuracy than that combined with the conventional sinc interpolation. Both the simulated data and the extracted GF-3 data experiment demonstrate the validity and accuracy of the proposed approach. Synthetic aperture radar (SAR) is a well-proven remote sensing technique for high-resolution imaging of the Earth’s surface, while it is independent of weather and illumination conditions. Swath width and resolution are two important performance specifications in the SAR system. However, the requirements of wide-swath imaging and high azimuth resolution cannot be satisfied in the meantime in the SAR system design. To control range ambiguities, the PRI must be larger than the time that it takes to collect returns from the entire illuminated swath which result in a lower bound of pulse repetition frequency (PRF). On the other hand, to avoid significant azimuth ambiguity levels, a large PRI or equivalently a low PRF implies the adoption of a small Doppler bandwidth and limits the achievable azimuth resolution. This has encouraged lots of research to focus on resolving the limitation of wide swath and high azimuth resolution ,2,3,4. IThe design of a PRI sequence with slow and fast change is analyzed in Ref. . The priThis paper is organized as follows: In The Conventional SAR systems usually employ a fixed PRI, or equivalently a fixed PRF. The value of PRF is restricted by many factors of the conventional SAR system. The azimuth ambiguity-to-signal-ratio (AASR) and range-ambiguity-to-signal-ratio (RASR) are highly related to the PRF value. A low value of PRF increases the AASR due to the azimuth spectrum aliasing effect. On the other hand, a high PRF value will reduce the interpulse period and result in overlap between the received pulses, thus leading to an increase of RASR. Furthermore, the PRF selection is constrained for a conventional SAR system because there is a single antenna for both transmitting and receiving processes. Also, the PRF is selected to ensure that the nadir return from succeeding pulses is excluded from the echo recording window, because the nadir return leads to possible saturation effects in imaging processing.The PRF restriction of transmit interference can be defined as follows:The range ambiguity restriction on PRF can be written as follows:The span of acceptable PRF values is, therefore, established by the aforementioned analysis. In general, with the off-nadir angle increasing, the available PRF span is reduced and the ambiguity-to-signal ratio is lowered. In the spotlight SAR, as the resolution and the off-nadir angle increase, the synthetic aperture time enlarges as well as the range migration amount. Therefore, the imaging-swath is further reduced, and there could be no acceptable PRF in a certain condition. As an example, for spaceborne SAR with spotlight mode, the sensor altitude is 1100 km, and the requirement of resolution and swath is 0.1 and 8 km × 8 km respectively. The excluded zones of PRF choice defined by Equations (1)–(2) are shown in Through the periodical PRF variation, the blind ranges are no longer fixed but uniformly distributed in the whole imaging swath. Therefore, the transmit and nadir interference are no longer constraints in the SAR system. Then, it is possible to achieve a high-resolution and wide swath by employing the PRF variation technique. Two types of PRI sequence can be chosen according to system demands, and the approach of establishing parameters for PRI sequences of slow change and fast change will be discussed in the following.The criterion of slow linear variation of the PRI sequence design is to minimize the PRI span to reduce the effect on range and azimuth ambiguities. To make the blind ranges distribute uniformly in the interested illuminated area, the acceptable PRF span between The design of slow linear variation of PRI would result in consecutive pulses losing. The principle to design fast change sequences of PRIs is to avoid missing two consecutive samples in the raw azimuth signal for all slant ranges of interest. According to principle , the difs losing , and it Finally, the sequence length Equation :(6)N≥NmiThe SAR parameters for both the fast variation and slow variation of PRI calculated by the Equations mentioned above are listed in In A bandlimited continuous signal can be reconstructed by employing a sinc interpolation ,15,16. Pith samples, and However, the nonuniform sampling signal or the non-baseband signal, which is the azimuth signal of SAR with PRI variation, cannot be reconstructed by the traditional sinc interpolation mentioned above. Moreover, the Doppler spectrum of the nonuniform sampling azimuth signal cannot be calculated by Fast Fourier Transform (FFT). A generalization of the Discrete Fourier Transform (DFT), i.e., NUDFT, can be employed to obtain the Doppler spectrum, which is:In terms of the azimuth pattern weighting, the main energy of Derived from Equation (9), we can obtain that:Comparing Equation (7) with Equation (10), the reconstructed expression of the nonuniformly sampled signal can be obtained as follows:The interpolation kernel is a sinc-like function L). The longer the length L is, the better the modified sinc interpolation performs in reconstruction in theory. In practice, an interpolation kernel that uses a large L would be very costly. Fortunately, the kernel weight decreases rapidly with the distance away from the interpolation point. Thus, length L can be shortened without much loss of accuracy. In the experiments of this paper, the desired results can be obtained while The tradeoff between accuracy and computational cost must be taken into consideration when selecting the length of the modified sinc interpolation kernel (denoted by Na is the total of sampling points in azimuth direction. The ratio of calculating the complexity of NUDFT to that of the modified sinc interpolation is The calculating complexity of NUDFT and modified sinc interpolation methods are shown in By beam steering in the azimuth direction, the spotlight SAR effectively achieves high-resolution images of the illuminated area ,18,19,20The SAR echo backscattered from a point target can be expressed as follows:To simplify the discussion, the signal can be transformed into range frequency and azimuth time domain, and then can be defined as follows:In the range frequency and azimuth time domain, the signal in each range gate has the form of a chirp-like signal, which is given by:To solve the spectrum folding problem, the first step of the procedure involves the azimuth convolution between the echo and the deramping chirp signal. The convolution can be asymptotically evaluated by applying the stationary-phase method, wherein the resulting signal depends on the product as follows:Then, the whole imaging processing block diagram is shown in For the nonuniformly sampled signal, the modified sinc interpolation is needed. After multiplying For spotlight SAR with continuous PRI variance, the deramp procedure of the two-step imaging algorithm is modified as follows:After that, the stripmap processing procedure is applied like the conventional two-step processing approach. The whole processing procedure is present in In order to validate the proposed method, a number of experiments have been carried out using simulated data and GF-3 data. The simulation results of 1 D azimuth signal are shown in this section to compare the accuracy and the efficiency between NUDFT, the conventional sinc interpolation and the modified sinc interpolation method. Furthermore, both of the two different linear sampling methods of fast and slow PRI variation given in The simulation results given in In The simulation results given in From The level of the false targets of the simulation results is summarized in To give an idea of the image quality improvement of actual SAR image, a GF-3 data, acquired over the city of Nanjing, China, has been used. As the raw data of GF-3 is uniformly sampled, data-preprocessing is employed to create nonuniformly sampled data . The datIn As is apparent, after data-preprocessing, the targets are still present in image, but the imaging quality is significantly affected by azimuth ambiguities, which is illustrated in To further figure out the problems of the false targets, which are caused by nonuniform sampling and spectrum folding effects, some sub-areas are extracted from To better clarify the effect of the modified sinc interpolation on point target, we choose a nonstandard point target on a ship, which is shown in From This paper focuses on the signal processing for spotlight SAR with continuous PRI variation and very high azimuth resolution. A modified sinc interpolation is proposed in this paper to reconstruct a uniformly sampled signal in a time domain. As the kernel weight decreases with the distance away from the interpolation point, the computational cost of the modified sinc interpolation is far less than NUDFT by choosing a suitable kernel length. Combined with the traditional two-step processing approach, the modified sinc interpolation is proposed to reconstruct the nonuniformly sampled raw data after azimuth deramping, which further expands the applicability of the two-step processing approach. The simulation results verify the validity of the proposed method. The modified sinc interpolation has better performance in dealing with a nonuniformly sampled signal than the conventional sinc interpolation; besides, the modified sinc interpolation reduces less computational resources compared to NUDFT. In fact, the modified sinc interpolation can also be applied to other nonuniform sampling SAR systems, such as azimuth multi-channel SAR, to improve the focusing performance.


A common fault in turbomachinery is rotor–casing rub. Shaft vibration, measured with proximity probes, is the most powerful indicator of rotor–stator rub. However, in machines such as aeroderivative turbines, with increasing industrial relevance in power generation, constructive reasons prevent the use of those sensors, being only acceleration signals at selected casing locations available. This implies several shortcomings in the characterization of the machinery condition, associated with a lower information content about the machine dynamics. In this work, we evaluated the performance of Continuous Wavelet Transform to isolate the accelerometer signal features that characterize rotor–casing rub in an aeroderivative turbine. The evaluation is carried out on a novel rotor model of a rotor–flexible casing system. Due to damped transients and other short-lived features that rub induces in the signals, the Continuous Wavelet Transform proves being more effective than both Fourier and Cepstrum Analysis. This creates the chance for enabling early fault diagnosis of rub before it may cause machine shutdown or damage. The flawless operation of rotating machinery such as turbomachines plays a key role in many branches of industry such as electrical power and heat generation, aerospace and naval propulsion, and manufacturing. As their performance levels have risen steadily in the course of time their margins of admissible operation have shrunk. A failure in any of these machines could cause considerable economical or even human losses. Thus, it becomes convenient to put in place a maintenance program which allows detecting any abnormality in the machinery operation at the early stages, before a fault at an advance stage forced it to be put out of duty.rotor transmits the mechanical power to or from an external power source or sink. The rotor contains circumferential arrangements of blades called disks attached to a rotating shaft. A casing built around the rotor sustains it and channels the working fluid passing through the machine with the aid of disks of vanes (https://www.power-eng.com/articles/2015/09/ge-announces-launch-of-latest-aeroderivative-gas-turbine-lm6000-pf.html). Optimal thermodynamical efficiency requires, among many other factors, most of the working fluid flow passing through the rotor blades with no leaks. To achieve this, the diametrical clearance between the rotor and the seals contained by the casing must be minimized, but the price to pay is a higher probability of rotor–casing rub. This phenomenon causes, when unnoticed, wear and overheating and, if severe, may be highly destructive. Even if modern industrial equipment counts with machine protection relays that shut the machine down in the case of faulty or abnormal duty, a better knowledge of the dynamics of faulty machines—in this case, rotor–casing rub—and more effective monitoring and protection systems lead to earlier diagnosis, shorter downtimes and lower operation and maintenance costs.In a turbomachine, a Rub dynamics, monitorization, detection and diagnosis of rub and other malfunctions have been research topics in academia for the last decades and industry has large experience on the matter ,2. RotorHowever, despite the industrial relevance of the problem, only a handful of papers have been published on the subject of the detection of rub with acceleration sensors on casing. The authors of ,4,5 showThe publications cited in the previous paragraph are centered on the same type of rub: with the infliction of a massive relative rotor–casing mechanical deformation at one or several fixed points, or by fitting an obstacle between rotor and casing, the authors reproduce a rub that extends through all or almost all the circumferential rotor disk blades. There is an interest in the study of lighter and more frequent types of rub such as partial, single-point rub  with a number of cylindrical rigid solid disks . In an aeroderivative gas turbine, the ends of a casing are attached to solid elements called frames, which also house the rotor bearings. These bearing-casing joints are modeled as very stiff bar trusses between each bearing and a number of homogeneously-distributed points in the casing . The casing rests on the ground through linearly elastic supports attached to several points of the casing  follows the rotor axial direction and the x and y axes are contained in a rotor radial plane at one of the shaft extremes. A positive rotor rotation speed follows the shortest path from x to y.The rotor–flexible casing model that has been developed  compriseorbit—is also of great interest because that vibration is what is monitored in conventional turbomachines as the indicator of malfunction.This rotor may vibrate due to the action of unbalance and rub forces that will be described further below. The motions caused by those forces are measured by one or several accelerometers on the casing (green) which yield casing acceleration versus time. The rotor radial motion—called the rotor This model can be adapted to any material properties, dimensions and numbers of disks, bearings and supports, as long as the model hypotheses hold. As shown in The model simulation requires the dynamical system of ordinary differential equations (SODE) shown in Equation . In thisS+D), casing (C) and bearings (B). The viscoelastic couplings between shaft and bearings and between bearings and casing are accounted for with the addition of elements outside the main diagonal to the global viscous damping and stiffness matrices:N is the total number of nodes. Simulations were carried out with a mesh of 19 shaft nodes, 18 shaft beam elements, 2 bearing nodes, 5490 casing nodes, and 2700 casing shell elements. The first step was a modal analysis of the free undamped system with Following , the sysThe two constants Campbell diagram shown in The variation of natural frequencies with rotation speed in the damped free rotor–flexible casing due to the speed-variable damping term of Equation  is reprei is:keyphasor mark . The unj. This obstacle may impact the rotor at node i. When the system is at rest, the clearance between rotor and obstacle is A number of rotor–casing rubs can be defined, each between a casing node and a rotor node . An obstFixed-point rub models such as this one have been studied in some publications: Ma et al.  and Behzj, its normal unitary vector equals the casing unitary normal vector at j, If the obstacle contact surface is flat and parallel to the casing at the attachment node The relative displacement The normal rub force results from the product of relative displacements and velocities with stiffness and damping contact coefficients i, the friction force at the rub spot inflicts, by balance of forces, a bending moment at the casing around the z axis. Normal and friction rub forces at rotor and casing are projected over the global coordinate axes, resulting in the following local rub vectors of rotor (node i) and casing (node j):x.Since the rub spot stands at a distance The model mesh counts with a total of 27,551 degrees of freedom, making a numerical integration of model Equation   . The say, J. W. ) is applcepstrum [spectrum of the spectrum, is a popular diagnosis tool in machinery condition monitoring. Generally, it is the inverse Fourier transform of the logarithm of a spectrum. In the case of the Real Cepstrum, its mathematical definition is:The cepstrum , also knrahmonics with a time-dimensional periodicity called quefrency, measured in seconds.First, the complex phase information of the signal Continuous Wavelet Transform (CWT) is the inner product of a function mother wavelet:a and b are, respectively, dilation and translation factors. The coefficient Analogously to the Continuous Fourier Transform  the Con wavelet  has been wavelet ,29,30,31synchrosqueezing frequency reassignment to the wavelet coefficients. This post-processing algorithm, described by Daubechies et al. in [To improve the resolution of the wavelet scalograms, we applied a t al. in , correcttime record being 2 s. The radial acceleration of casing node j, x and y degrees of freedom as The simulated rotor–casing model comprises two disks symmetrically attached to the shaft. The second disk contains an unbalance mass tacle in , cR=0 beIt is common practice to integrate the accelerometer signals, monitoring velocity instead of acceleration with respect to time. The purpose is to attenuate the high-frequency noise contained in the accelerometer signal and to highlight the low-frequency band of the spectrum, which is the source of information that is most commonly used for protection purposes in rotating machinery . TherefoFrom the Campbell diagram , the firter 2 of ,17,19.In Every time the rotor impacts the casing, two impulse peaks appear in the acceleration plot c: the fiA single-point rub regime is easy to identify in the full spectrum plots b: it manIn the following sections, the signal processing methods described above are applied to the casing signals from the rotor with light rub  to isolaThe Fourier spectra of the acceleration and velocity records under single-point rub are shown in The cepstrum analysis of the downsampled and filtered acceleration and velocity signals  underlinThe acceleration and velocity data were decomposed into wavelet coefficients with the Morlet wavelet function. First, the 2 s long time records were low-pass filtered and resampled to 3.2 kHz, resulting in two sampling vectors with 8000 samples. Then, only the last 160 samples of both vectors—with a length of 0.1 s, equivalent to six shaft rotation cycles at 3600 rpm—were picked for the calculation of the wavelet coefficients, discarding the rest. As mentioned above, a synchrosqueezing algorithm was applied to the coefficients for improved resolution. The 0–800 Hz acceleration and velocity scalograms representing coefficient absolute values with a colored scale are shown in The two scalograms clearly highlight the fundamental rub frequency of 30 Hz and its lowest multiples, with the 3× harmonic—90 Hz, near the second shaft bending mode in fft and wsst with the samples inputs.Even though the CWT input vectors, with 160 samples, are far shorter than the DFT input vectors, with 56,000 (acceleration) and 4000 samples (velocity), the calculation of CWT coefficients is considerably slower than the calculation of the spectra. Nevertheless, since a more effective detection of rub can be carried out with much shorter sampling vectors, with lower acquisition times, the balance tips on the side of the CWT as a preferable monitorization tool.In this work, we presented a model of an aeroderivative gas turbine for the simulation of abnormal duty. In particular, it succeeds in reproducing a common type of rub encountered in conventional turbomachinery, the supercritical partial single-point rub with period-two (See chapter 2 of [This rub is reflected as impulse trains in the casing acceleration and velocity signals . Each imThe Fourier spectra of the signals are mainly comprised of impulse trains with fundamental frequency equal to the impact frequency: half the rotor rotation speed . The higThe Fourier spectra and the cepstra in The visualization of those short-lived pieces of evidence of rotor–casing rub in a Fourier spectrum would require collecting very large sampling vectors with large time intervals between the first and the last sample to improve frequency resolution as much as needed without worsening the spectrum frequency range. The acquisition of large data sets is time-consuming and comes with a loss of precocity in the diagnosis. On the other hand, the Continuous Wavelet Transform has the potential to identify rotor–casing rub with the analysis of only a few impacts in a very short time span with no more than a small processing time penalty, as shown in


Lane detection is an important foundation in the development of intelligent vehicles. To address problems such as low detection accuracy of traditional methods and poor real-time performance of deep learning-based methodologies, a lane detection algorithm for intelligent vehicles in complex road conditions and dynamic environments was proposed. Firstly, converting the distorted image and using the superposition threshold algorithm for edge detection, an aerial view of the lane was obtained via region of interest extraction and inverse perspective transformation. Secondly, the random sample consensus algorithm was adopted to fit the curves of lane lines based on the third-order B-spline curve model, and fitting evaluation and curvature radius calculation were then carried out on the curve. Lastly, by using the road driving video under complex road conditions and the Tusimple dataset, simulation test experiments for lane detection algorithm were performed. The experimental results show that the average detection accuracy based on road driving video reached 98.49%, and the average processing time reached 21.5 ms. The average detection accuracy based on the Tusimple dataset reached 98.42%, and the average processing time reached 22.2 ms. Compared with traditional methods and deep learning-based methodologies, this lane detection algorithm had excellent accuracy and real-time performance, a high detection efficiency and a strong anti-interference ability. The accurate recognition rate and average processing time were significantly improved. The proposed algorithm is crucial in promoting the technological level of intelligent vehicle driving assistance and conducive to the further improvement of the driving safety of intelligent vehicles. The annual increase in car ownerships has caused traffic safety to become an important factor affecting the development of a city. To a large extent, the frequent occurrence of traffic accidents is caused by subjective reasons related to the driver, such as drunk, fatigue and incorrect driving operations. Smart cars can eliminate these human factors to a certain extent ,2,3. In At present, lane detection is mainly based on visual sensors. Visual sensors have essentially become the eyes of a smart car that capture road scenes in front of vehicles through cameras. Such sensors can work continuously for long periods of time with strong adaptability. At the same time, visual sensors have a wide spectrum response range that can see infrared rays, which are invisible to the naked eye; this feature remarkably enlarges the vision space of human beings ,9,10,11.In this study, a lane detection algorithm for intelligent vehicles in complex road conditions and dynamic environments was proposed. Firstly, converting the distorted image and using the superposition threshold algorithm for edge detection, an aerial view of the lane was obtained by using region of interest (ROI) extraction and inverse perspective transformation. Secondly, based on the curve model, the random sample consensus (RANSAC) algorithm was adopted to fit the curves of lane lines, and the fitting evaluation and the curvature radius calculation on the curve were then carried out. Lastly, by using the road driving video under complex road conditions and the Tusimple dataset, simulation test experiments for lane detection algorithm were carried out. By analysing the experimental results and comparing with other algorithms, the comprehensive performance of the algorithm was evaluated.The rest of this paper is organised as follows: The detection image was captured by a camera mounted on a smart car. Although the camera lens enables the rapid generation of images, such images lead to distortion. In practical terms, distortion changes the shape and size of the lane, vehicle and background in the road scene. These changes are not conducive to judging the correct driving direction and determining the exact location of the vehicle. Consequently, converting of image distortion is essential. In this section, converting of image distortion includes camera calibration and image distortion removal.Instead of focusing on the principle of aperture imaging, the vehicle-mounted camera uses a lens that can focus a large amount of light at one time. These rays bend to varying degrees at the edge of the camera lens and produce the distorted image with edge distortion. The actual road scene is a three-dimensional space, but the collected detection image is a two-dimensional image. Therefore, it was necessary to establish a geometric model between the world and image coordinates and accomplish the camera calibration by obtaining camera characteristic parameters, so as to realize the converting of image distortion.wXwYwZwO, Camera Coordinate cXcYcZcO, Image Physical Coordinate 1xyO, and Image Pixel Coordinate ouvO. p is the projection point of point P on the image plane under the ideal linear model, and point d is the projection point of point P on the image plane when image distortion occurs.In the process of describing the geometric relationship of images in the three-dimensional visual space, four coordinates must be defined: World Coordinate The two-dimensional image captured by the vehicle-mounted camera must be sequentially converted between the respective coordinates in turn to realise the coordinate transformation of a certain pixel point in the image from the image pixel coordinate to the world coordinate. p is presented as follows:u0, v0) is the coordinate of point p in the Image Pixel Coordinate; dX and dY are the physical dimensions of each pixel in the Image Pixel Coordinate; f is the focal length of the camera; R is a unit orthogonal matrix of t is a translation vector representing the position relationship between the coordinates;  is the homogeneous coordinate of point p in the World Coordinate.The transformation relationship between the world coordinates of any point P in a three-dimensional space and the image pixel coordinates of the projection point f to the physical dimension of a pixel in the u-axis direction. Define f to the physical dimension of a pixel in the v-axis direction. Then, the above formula can be equivalent to:Define M1 is a u0 and v0. These four parameters are related to the internal structure of the camera called the internal parameters of the camera. The rotation matrix R and the translation vector t are determined by the orientation relationship between the camera and the world coordinates. Therefore, M2 is called the external parameters of the camera. The internal and external parameters of the camera were obtained through multiple experiments and calculations, and the process of camera calibration was completed.In recent years, vehicle-mounted cameras often used wide-angle lens to obtain an enlarged field of vision, and the image distortion changes appeared remarkable. Image distortion is generally divided into radial and tangential distortions. Compared with the actual road scene, the common edge distortion of lanes, vehicles and backgrounds is called radial distortion. If the camera lens is not parallel to the image plane of the visual sensor, the collected image will be tilted, thus making the lane, vehicle and background look closer or farther than in the actual three-dimensional world. This type of image distortion is called tangential distortion, which is more disadvantageous to reflect the real driving environment.r2 = x2 + y2,  and (4) demonstrate that image distortion is related to five parameters—Edge information is an important feature of the detection image. A suitable edge detection algorithm that can remove a large amount of useless data is beneficial to determine the basic outline of the lane. The inverse perspective transformation converts the detected image into the aerial view to recognise the lane at the optimal visual angle. Therefore, edge detection and inverse perspective transformation are crucial parts in image processing.Commonly used edge detection algorithms include global extraction methods based on energy minimisation criterion  and edge derivative methods that use differential operators . However, the traditional single-edge detection algorithm has many problems, including a too-wide detection range, poor antinoise interference and prolonged calculation time ,41,42. MThe Sobel operator is a type of discrete first-order difference operator. The influence of adjacent points in the neighbourhood is different for the current pixel point. Greyscale weighting and differential operations were performed on neighbourhood pixels to obtain the gradient and normal vectors of the pixel point that can be used to calculate the approximate value of the image brightness function.The Sobel operator performs edge detection on the detected image from the horizontal and vertical directions and can sufficiently filter the interference noise with the improved image processing effect. However, if only the Sobel operator is used for edge detection, then problems such as low detection accuracy and rough edges easily occur. These issues must be solved effectively.Compared with the RGB colour space, the HSL colour space can better reflect the visual field perception characteristics of the naked eye. Each colour channel in the HSL colour space can be processed independently and separately. Among them, the component image with S channel performs best and is beneficial to reducing the workload of image processing remarkably and significantly improving the target recognition rate of the detected image.x direction is superimposed with the colour threshold of the HSL colour space S channel, and the superposition result is shown in Gradient threshold segmentation based on the Sobel operator and colour threshold segmentation based on the HSL colour space have advantages and disadvantages. The gradient threshold of the Sobel operator in the x direction and the colour threshold segmentation result of the HSL colour space S channel are represented by green and blue, respectively. After edge detection, substantial redundant information, such as the sky, trees and vehicles, still remain in the image. The two-lane lines that appear near-wide and far-narrow gradually meet and make it difficult to detect the lane at a later stage. Therefore, performing ROI extraction and inverse perspective transformation on the detected image is necessary.Given that the vehicle-mounted camera was installed in the middle of the roof of the smart car at a certain depression angle, the detection image contained useless background information, such as the sky, trees and hillsides, on both sides of the road. The effective detection portion, such as the lane, can account for approximately two-thirds of the area of the detected image called ROI. ROI extraction of the detected image can reduce the unnecessary computation and shorten the consumption time of the subsequent image processing step. Perspective is the phenomenon of images. The closer you get to the camera, the bigger it looks and vice versa. Parallel lane lines merge into a point in the distant field of vision called the vanishing point. The distance between the adjacent lanes near the vanishing point decreases gradually, which is detrimental to effective lane detection. Inverse perspective transformation is based on the inverse coordinate transformation from the world coordinate to the image coordinate that transforms the perspective image into the aerial view and restores the parallel relationship between the lane lines ,44.Lane detection in complex road conditions is susceptible to external environmental factors, such as lack of light, road tortuosity and vehicle obstruction. The previous image processing was based on a single detection image. However, effective lane detection must be applied in dynamic driving environments while maintaining a recognition rate with sufficiently high accuracy. In this section, the mask operation of the lane was firstly carried out. Then, on the basis of the third-order B-spline curve model, the RANSAC algorithm was used to achieve accurate fitting and curvature calculation of the lane. Lastly, simulation test experiments were performed based on road driving video and the Tusimple datasets, the experimental results were analysed, and the performances of algorithms were compared.In the aerial view of the lane, useless interfering pixels still existed. Such interference prolongs not only the image processing time but also easily causes false detection in the next lane detection. Therefore, before lane detection, masking the detected image was necessary. Mask operation essentially filtered the pixel points to highlight the target lane in the detected image.The mask operation formula is defined as follows:Mask operation clearly shows the target pixel point by weighting and averaging the pixels around the target pixel that contributes to sharpening the detection image. n-order B-spline curve is defined asn-order basis function presented as follows:An In the actual road scene, considering that the lane under complicated road conditions tend to be tortuous and variable, the third-order B-spline curve model was used to fit the lane lines. The mathematical expression corresponding to the third-order B-spline curve is as follows:i = 0, 1, 2, 3 into Equation (7) separately, the above equation is converted toBy substituting p0, p1, p2 and p3 correspond to the four control points of the third-order B-spline curve, which can be adjusted accordingly based on real-time road conditions.This equation is then expressed as the following matrix:The RANSAC algorithm is a type of random sampling consistency algorithm. Firstly, random points were obtained from a large number of observation data, and the valid points that met the hypothesis requirements were reserved. The invalid points that failed to meet the hypothesis requirements were discarded. Secondly, the valid points were used to estimate the corresponding models, and the optimal parameters of the estimated model were obtained through continuous iteration. Lastly, the estimation model was accurately fitted based on the obtained effective parameters ,46.(1)Search for the pixel points whose grey value is not equal to 0 in the image to be detected, and the data point set S required by the algorithm is obtained.(2)According to the third-order B-spline curve model, randomly select four points as the initial valid points of curve fitting in the data point set S, and then an initial third-order B-spline curve is obtained.(3)d are close to the fitting curve, and then the points are added to the valid point set Q as new valid points.Calculate the relative distance between the remaining data points and the initial third-order B-spline curve. Data points that do not exceed the distance threshold (4)n of the valid points in the preset curve model, step (5) is executed. Otherwise, steps (2) and (3) are repeated until the number of valid points meets the requirements or the upper limit k of iteration times is reached.When the number of data points in the valid point set Q reaches the threshold number (5)k of iteration times is reached, the algorithm terminates.The third-order B-spline curve is refitted by using the data points in the current valid point set Q, and the best curve fitting result is preserved. When the upper limit As can be seen from the above figure, the basic steps for lane line fitting via the RANSAC algorithm are as follows:The RANSAC algorithm can reduce the interference of invalid points in curve fitting, and the curve model can be re-estimated by the continuous accumulation of valid points. With the increasing number of iterations, the obtained fitting curve gradually tends to be the best and minimises the error between the fitting curve and the real lane line. The RANSAC algorithm based on the third-order B-spline curve model was used to fit the lane lines. This algorithm can describe lane lines with different shapes and has good adaptability and robustness.The RANSAC algorithm uses the continuous iterative method to obtain the optimal fit curve. Therefore, determining an effective evaluation criterion for lane line fitting is necessary. The comparison of the error rate magnitude between the fitting curve and the real lane line determines the best lane line fitting result. Score) is defined as the reciprocal of the mean of the relative distance between all data points in the valid point set Q and the fitting curve:n is the number of all data points in the valid point set Q.When the distance from all valid points in the area around the fitting curve to the fitting curve was the smallest, the error between the fitting curve and the real lane line was minimised, and the lane line fitting evaluation score was the highest. The following evaluation score (m). The curvature calculation of the third-order B-spline curve is more complicated than that of the simple curve. In this study, the original curve was reduced in order, the first and second derivative curves re-obtained by first- and second-order reduction, respectively. In the two-dimensional plane, let the coordinate corresponding to the first derivative be The curvature of the current lane line was used to express its curve degree. The reciprocal of the curvature is the curvature radius, which was used in this study to represent the curvature  Core (TM) i5-6500 CPU@3.20GHz processor, 8.00 GB memory, 2 TB mechanical hard disk.To verify the recognition performance of the lane detection algorithm in complex working conditions and dynamic environments, road driving videos were used to carry out the simulation test experiment in this work. Such videos in the experiment were collected by using a real-time vehicle-mounted camera, and the lane lines were detected for different road conditions, such as highway, mountain road and tunnel road.Furthermore, the classical sliding window search method was utilised to test the lane detection algorithm dynamically in the simulation test experiment. Firstly, a pixel histogram was generated by the pixels whose grey value was not equal to 0, and the peak value in the pixel point set was obtained (the area where the lane line exists). Secondly, the sliding window was used to accumulate from bottom to top. When the number of pixels in the window exceeded the set threshold number, the mean value was taken as the centre of the next sliding window. In addition, by using the sliding window search method, the offset of the vehicle relative to the centre position of the road could be estimated.In the lane detection test experiment, the accurate recognition rate under highway condition reached 99.15%, and the average processing time per frame was 20.8 ms, thereby indicating that the lane detection algorithm had good real-time performance and accuracy. The accurate recognition rate under tunnel road condition reached 98.47%, and the average processing time per frame was 21.6 ms, thereby indicating that the lane detection algorithm still had good adaptability in case of insufficient light. The accurate recognition rate under mountain road condition reached 97.82%, and the average processing time per frame was 22.1 ms, thus indicating that the lane detection algorithm still had good robustness and antijamming ability in the case of road tortuosity and background interference. By sorting and analysing false or missed detection images, the majority of these images were caused by motion blur, vehicle occlusion, insufficient light and excessive road bending. In the future, improving the lane detection algorithm will be necessary to enhance its complexity and efficiency. Collecting road traffic videos with varied road conditions will also be important to improve the inclusiveness and robustness of the lane detection algorithm continuously.In order to further test the comprehensive performance of the proposed algorithm under a variety of complex road conditions, in addition to the road driving videos for simulation test experiments, the Tusimple dataset  was also used for lane detection. The Tusimple dataset consists of 3626 training images and 2782 testing images, and each sequence image comprising 20 consecutive frames taken in 1s, of which the first 19 frames are unmarked and the 20th frame is labelled with lane ground truth. The images in the dataset can be roughly divided into four conditions, including different weather conditions, daytime, lanes number (2 lanes/3 lanes/4 lanes or more), and traffic environments ,48. 150 It can be seen from To verify the performance of the lane detection algorithm, the proposed algorithm was compared with other algorithms used in the literature. In this paper, the proposed algorithm was compared with traditional detection methods and deep learning-based methodologies. In particular, the proposed algorithm and reference  and 52]52] all cThis study proposed a lane detection algorithm for intelligent vehicles in complex road conditions and dynamic environments. Firstly, converting the distorted image and using the superposition threshold algorithm based on the Sobel operator and HSL colour space for edge detection, an aerial view of the lane was obtained by using ROI extraction and inverse perspective transformation. Secondly, the RANSAC algorithm was adopted to fit the curves of the lane lines on the basis of the third-order B-spline curve model, and the fitting evaluation and the curvature radius calculation on the curve were carried out next. Lastly, by using the road driving video under complex road conditions and the Tusimple dataset, simulation test experiments for lane detection algorithm were performed. The experimental results show that the average detection accuracy based on road driving video reached 98.49%, and the average processing time reached 21.5 ms. The average detection accuracy based on the Tusimple dataset reached 98.42%, and the average processing time reached 22.2 ms. Compared with traditional methods and deep learning-based methodologies, this lane detection algorithm had excellent accuracy and real-time performance, high detection efficiency and strong anti-interference ability. The accurate recognition rate and average processing time were significantly improved.In terms of lane detection accuracy and algorithm time-consuming, the proposed lane detection algorithm had clear advantages. It was conducive to greatly enhancing the driving safety of intelligent vehicles in the actual driving environments and effectively meeting the real-time target requirements of smart cars and played an important role in intelligent vehicle driving assistance. In the future, the inclusiveness and anti-error detection of the lane detection algorithm can be further optimised and improved to exploit the overall performance of the algorithm.


Landfill site’s selection represents a complicated process due to the large number of variables to be adopted. In this study, an arid area (Babylon Governorate as a case study) was selected. It is located in the middle region of Iraq. In this area, the landfills do not satisfy the required international criteria. Fifteen of the most significant criteria were selected for this purpose. For suitable weight for each criterion, the multi-criteria decision-making (MCDM) methods were applied. These methods are AHP and RSW. In the GIS software 10.5, the raster maps of the chosen criterion were arranged and analyzed. The method of change detection was implemented to determine the matching pixels and non-matching pixels. The final results showed that there are two candidate locations for landfills for each district in the governorate (ten sites). The areas of the selected sites were sufficient to contain the cumulative quantity of solid waste from 2020 until 2030. Selecting an adequate site for landfill is necessary to protect human and environment. To determine the proper site for disposal of solid waste optimally, the decision-makers need wide expertise to evaluate the lands within the study area that conforms to the requirements of environmental and scientific factors and the regulations and determinants of local and central governments. In addition, the selection site for a landfill should meet the following factors like rapid economic growth, social, population growth rate, improvements in living standards, growing environmental awareness, and government and municipality funding  and the risk to human health.Inhibiting groundwater and surface water contamination by the leachate from landfill sites.Eliminating the effects of burning waste on human and surrounding environment.Controlling the gas emissions from landfill.Reducing the negative impacts on the environment and human population  and ratio scale weighting (RSW).Analytical hierarchy process (AHP) is a preferred method in multi-criteria decision-making methods. Thomas Saaty originally developed it in 1980. It is used to estimate the consistency weightings of criteria that resulted from constructing the matrix of pair-wise comparisons. In literatures, several studies used the analytical hierarchy process (AHP) method with GIS software in their studies to determine the weightings of criteria in the selecting sites for landfills  was used to obtain the weightings of criteria by allocating a proportion value for each criterion that is deserved through the decision-makers based on previous studies in this field and the opinion of experts.In previous studies, several candidate landfill sites were identified in different areas using the ratio scale weighting (RSW) method and GIS . In addition, the comparison method (change detection) was used to find the pixel percentage of matching and non-matching for the two raster maps of multi-criteria decision-making methods, and to verify the convenience of the chosen locations for the landfill on both output maps, AHP and RSW methods were used.2. Administratively, Babylon Governorate is divided into five major cities (district) referred to as Qadhaa. These districts are Al-Hillah , Al-Hashimiyah, Al-Musayiab, Al-Mahawil, and Al-Qasim. These districts include 16 smaller cities, which are called Nahiah.In the central part of Iraq, Babylon Governorate is located approximately 100 km to the south of Baghdad  . On the other hand, buffer zones should be created around or on both sides of specific geographic features for each criterion in the GIS software. Therefore, the site restrictions and buffer zones are necessary to protect the human health and to avoid any risk to the environment, as well as to fulfill the requirements of administrative regulations  according to the internal reports of the Iraqi Ministry of Education  Buringh . AccordiThe third source includes the implementation of the spatial interpolation method “kriging” within spatial analysis tools in ArcGIS between defined readings. The map of groundwater depths was produced using this process where data from 185 wells distributed in the governorate  was given the highest rating, while the lowest value of groundwater depth  was given the lowest rating Fig. . In liteIn the current study, buffer zones of ≤ 5 km were assigned a rating of zero Şener . For bufThe classification of urban centers’ map was adopted to take into consideration the economic factors (transport and cost of land), as well as to protect the people and surrounding environment from negative impacts that results from the cumulative waste in landfills . Moreover, the potential to expand the urban areas in the future was also considered. In addition, there is always an increase of social opposition to establishing landfills  was used  of the study area was used to create the map of “slope.” Most of the land in the governorate has a slope of less than 5°, and it was given a score of 10 Fig. . The ranThe “agricultural land use” map in Babylon Governorate includes three categories . The category of unused land was given the highest possible score of 10. The “orchards” and agricultural land were given a value of 5 and zero, respectively. This is to protect agricultural land from destruction and contamination Fig. .In Babylon Governorate, there are many important archeological and religious sites. In this study, a value of zero was assigned for the buffer zones of ≤ 1 km from the archeological and religious sites in all directions  and ratio scale weighting (RSW). These methods can be summarized as follows:Saaty  developeIn the AHP method, the matrix of pair-wise comparisons was created to derive the relative weights of criteria Fig. . In the To check the consistency between the resultant weights for criteria, the value of the consistency ratio (CR) was computed through using the following formula: (CR = CI / RI) Saaty . In the The consistency is acceptable when the value of the consistency ratio is less than 0.1. Therefore, the CR value was 0.027 and smaller than 0.1.The second method which was applied in this study was the ratio scale weighting (RSW) method. In this method, the weights of criteria are given directly by decision-makers based on previous studies in this field. In this method, the decision-makers are giving a convenient proportional value for each criterion. A value of 100 is assigned to the most important criteria to be the base value for the other criteria. Each criterion is given the proportionally value smaller than 100 according to its importance relative to other criteria. The criteria are arranged proportionally from the most to the lowest significant Şener . Table 4To calculate the standard weights (SWi) in the ratio scale weighting (RSW) method, the proportional weight value for each criterion was divided by the value of proportional weight for the lowest importance criterion. The standard weights represent the new weights for each criterion.i is the relative weight for each criterion; SWi is the standard weights of each criterion of area i under criterion j; n is the criteria number.The standard weights of criteria were converted to relative weights through divided each criterion standard weight by their summation, using Eq.  as folloIn order to implement the analysis process for producing the final map of landfills in GIS, all vector maps were converted to the raster maps. After producing the weightings for the 15 raster maps of criteria from AHP and RSW methods Table  as folloMi is the index of suitability for area i; n is the number of criteria; CWk is the relative weighting of each criterion; SCik is the rating value of area i under criterion k.Table According to Jin et al. , the U.SIn this context, four categories exist. These are (i) most suitable areas (MSA), (ii) suitable areas (SA), (iii) moderately suitable areas (MDSA), and (iv) unsuitable areas (USA) The annual increment rate of (1%) for waste generation rate (WGR) starting from the year 2013.(ii)Solid waste generation rate for Babylon Governorate in 2013 (SWGR).(iii)The expected population for the year (2030) was built based on the existed population in 2013 and using the annual growth rate of 2.99% (Iraqi Ministry of Planning This equation was constructed based on three factors. These are:r)( is the solid waste cumulative quantity for the particular year (tonne); SWQrt)( is the solid waste quantity for the particular year (tonne); SWCQrt−1)( is the solid waste cumulative quantity for the previous year before the particular year (tonne).The solid waste cumulative quantity during the years from 2020 to 2030 in Babylon Governorate and its districts was estimated using Eq. . The solThe volume of waste in the year 2030 and the cumulative waste volume from 2020 to 2030 in the governorate and its districts are shown in Table The data are given in Table −3)  and methods of AHP and RSW. Thus, 15 maps of criteria were entered into the GIS to produce the final map for landfill siting. The 15 layers are groundwater depth, urban centers, rivers, villages, soil types, elevation, agriculture lands use, roads, slope, land use, archeological sites, gas pipelines, oil pipelines, power lines, and railways.Two MCDM methods were implemented in different styles to find the relative weights for each criterion. The analytic hierarchy process (AHP) was the first method, where a matrix of pair-wise comparisons between each criterion to derive the weight to each criterion was used. The second method was the ratio scale weighting (RSW). This method is based on the experts’ opinion and previous studies in this field by giving proportion values for each criterion according to its importance among other criteria. Then, the special analysis tool in GIS “Map Algebra” was used to generate the final map to select the candidate sites for landfill for each method.The two final maps that resulted from the two methods of MCDM (AHP and RSW) were combined in the GIS. Then, the change detection method was used to find the matching and non-matching areas on the final raster maps of AHP and RSW methods. The comparison process of the change detection method was applied to check the appropriateness of the landfill sites that were selected in Babylon Governorate on the two maps that were produced from the AHP and RSW methods.Finally, ten candidate sites were obtained on the final maps for landfill in Babylon Governorate among several sites (two for each district). All the selected sites were located within the category of “most suitable” on the final maps of MCDM methods and within the matching areas in the comparison map. It was found that these sites are suitable to accommodate the cumulative solid waste for the years 2020–2030. This procedure will allow the planners and decision-makers to apply it in other areas in Iraq that have similar conditions  when selecting a new landfill site.