This paper focuses on the frequency coded chipless Radio Frequency Identification (RFID) wherein the tag’s information bits are physically encoded by the resonators’ notch position which has an effect on the frequency spectrum of the backscattered or retransmitted signal of the tag. In this regard, the notch analytical model is developed to consider the notch position and quality factor. Besides, the radar cross section (RCS) mathematical representation of the tag is introduced to consider the incident wave’s polarization and orientation angles. Hence, the influences of the incident wave’s orientation and polarization mismatches on the detection performance are quantified. After that, the tag measurement errors and limitations are comprehensively explained. Therefore, approaches to measureing RCS- and retransmission-based tags are introduced. Furthermore, the maximum reading range is theoretically calculated and practically verified considering the Federal Communications Commission (FCC) Ultra Wideband (UWB) regulations. In all simulations and experiments conducted, a mono-static configuration is considered, in which one antenna is utilized for transmission and reception. Recently, chipless Radio Frequency Identification has achieved a great importance in the research communities due to the tremendous possible applications ,2,3. HowOn the other hand, the chipped and chipless RFID technologies are identified using far field radio waves which operate at different frequency ranges, from low frequency (LF) to ultra-wide band (UWB) . Near fiThe work introduced in this paper is focused on the FC chipless tags. The FC tags are classified into two main groups based on their structures. The first group constitutes radar cross section (RCS)-based tags, and the second group constitutes retransmission-based tags . An RCS-Of the state-of-the-art, several tag designs are available for both categories. They are orientation dependent, and most of them are polarization sensitive. The tag’s angular dependency has not been previously studied in the literature. Furthermore, the maximum detectable angular ranges are not elucidated from the simulation and measurement points of view. Consequently, the detection performance degradation is not quantified. Therefore, this paper aims to fill this gap, and also to present approaches to counteract the incident wave mismatches. In addition, the reader’s coverage is theoretically estimated and practically verified while considering the FCC regulations. However, in the literature, a certain reading range is normally reported without giving any further details about regulations.The paper is organized as follows. The notch analytical model and the notch detection technique we utilized are introduced in In this section, the notch analytical model and the notch detection algorithm we applied are introduced.The chipless RFID tag’s response consists of several notches in the frequency domain with predefined resonators, quality factors, and notching frequency positions. According to filter theory , the notEquation ; and theThe notch bandwidth Equation .(2)Bn=fSimilarly, the notch pattern could be expressed as a function of frequency location Equation . HoweverThus, the notch pattern Consequently, the notch is modulated by a specific bandwidth at a certain frequency location to codify a predetermined code (bitstream) Equation .(4)Γ tag, shown in The tag-ID is configured to have the widest notch at the lowest frequency position, and the narrowest notch at the highest one, as shown in Notch detection algorithms are used to determine the existence of a notch in the backscattered signal from the tag. The signal processing involved in the notch detection is quite challenging, since the received signal power is very weak and is dramatically affected by undesired interference, environmental clutter, and noise caused by the receiver. Furthermore, manufacturing defects on the tag’s side may cause the notch to shift its frequency position or even change its shape. Another factor is the transmitting and/or the receiving antenna frequency response, which is superimposed on the received signal, as this also could modify the notch shape. All those factors could render the FC chipless RFID tag undetectable.In this work, a matched filter notch detection technique is implemented to detect the ID of the interrogated tag. This will show the effects of different tag displacements, angular and range-related, on the detection probability of the tag notches. Matched filter is an ideal filter which calculates the maximum SNR  of a received signal in the presence of additive stochastic noise . It is cThe algorithm works in three stages: The first stage is to obtain the matched filter response based on the RCS response of the tag. In each frequency range where a notch could exist, a matched filter response is created. The second stage is windowing the received signal and convoluting it with its respective predetermined matched filter. A decision is then made in the third stage, based on a predetermined threshold level.k is number of samples in the window; N is total number of windows, which also corresponds to the number of notches; The modified received signal Equation .(6)Wn(fEquation .(7)YnrraFor both tag types, the reading methodology which is presented in  is utiliConsider that the receiver sensitivity is –80 dBm. As a consequence, the maximum theoretical reading range for the RCS tag will be 3 m, in which the notch dynamic range is 3 dB, as shown in This section describes the measurement errors which limit chipless tag detection. Basically, the measurement errors are produced from the amplitude phase statistical noise and from the reader systematic errors. The statistical noise could be reduced by averaging over the several measurement cycles. Moreover, the systematic error could be modeled to calculate the tag’s frequency response accurately .Fundamentally, the first systematic error is the component matching, which is not uniform with frequency, like the antenna matching with couplers, switches, and so on. The second major limitation is the reader’s circuit leakage channels. The third measuring error appears from the nonlinear circuit of the reader and the antenna’s finite polarization purity. Therefore, the minimization of these realistic imperfections is of the utmost import when in comes to accurately measuring the RCS tag and enhancing the reader’s coverage.In this regard, the mathematical models of these error terms are introduced. Hence, the reader functions are mathematically described in The Vector Network Analyzer reader is equipped in the first block; the transmitter path is represented by the second block; the tag inscribed metallic scatterer is represented by the third block; and lastly, the receiver path is represented in the fourth block, as described in Therefore, the measured scattering matrix could be calculated from these transmitted and received signals based on Equation .(12)b_hThe measured scattering matrix is related to the tag correct scattering matrix Equation .(13)S_mEquation .(14)S_hHence, the correct scattering matrix n errors ,30. If tThe unknown error terms could be calculated from the measurement of reference targets with known scattering matrix S_c . Thus, tEquation .(16)S_mThe goal now is to determine these multiplicative error terms. Therefore, reference targets with known RCS could be utilized for calculating the multiplicative error terms. Therefore, a single reference algorithm is utilized for calculating the error coefficients with the knowledge of the scattering matrix of one target. The algorithm assumes that the cross-polarization signals are negligible .Hence, the correct RCS tag could be calculated by utilizing one known reference target measurement besides the empty room calibration. However for the retransmission tags, these assumptions are not valid, since the tag response is configured in the cross-polarized plane. Therefore, the depolarizing error terms should be considered. In this regard, a reference depolarizing tag is designed to calibrate the measurements of the retransmission tag.In this section the experimental results for the previously discussed scenarios are introduced. Therefore, the calibration procedures for both RCS and depolarizing tags are presented first. Then, the angular displacement measurements are demonstrated. Finally, the maximum reading range was experimentally determined, while considering the FCC regulations.The mono-static measurement setup can be seen in We followed the calibration procedures which are described in Utilizing the empty room calibration the measured backscattered reflection is expressed in Equation .(18)S_hHence, a perfect conducting sphere of Regarding depolarizing error terms, a reference tag is designed to be used for calibration. The calibration tag consists of two orthogonally polarized antennas which are connected through a coplanar transmission line. On the other hand, for the coded tag, the two antennas are connected through a multi-stop band filter that realizes the tag-ID as shown in For measuring the retransmission tags, the two orthogonally polarized channels of the horn antenna are utilized. The cross polarization isolation is more than 30 dB, which is the highest possible with single antenna. Consequently, the reader non-ideal depolarizing terms are much lower than the tag response after doing the empty room calibration. Considering that the incident wave is horizontally polarized, the tag response is configured in the vertical polarization plane and the measured scattering matrix is simplified in Equation .(19)S_vUtilizing the empty room calibration, the measured depolarized retransmission is expressed in Equation .(20)S_vAfter that, the calibration tag is utilized for calculating the multiplicative error terms, as explained in Equation .(21)R_vTherefore, the relevant depolarizing errors of the tag antennas are minimized, and the retransmitted response of the tag-ID can be detected. The calibrated measured tag response is shown in The angular displacement in the elevation plane is measured at three different angles, as explained in As previously mentioned, the azimuth displacement produces a polarization mismatch between the tag resonators and reader antenna. Therefore, a linear polarized tag was designed and manufactured to practically assess the performance degradation due to polarization mismatching. The tag consisted of half wavelength dipoles which resonated at The notch depth decreases with the increment of the polarization misalignment angle. However, the notch’s decrease in the co-polarized plane increases the notch level in the cross-polarized plane. It is concluded from these results that the elevation misalignment severely reduces the RCS value of the tag response, and this reduction is not uniform overall the tag response. The reason is that the higher frequency notches are exposed to more path loss. Therefore, the expected reading range is less. On the other hand, the azimuth misalignment only affects the notch’s dynamic level. Moreover the polarization mismatch problem could be easily solved by employing a dual-polarized antenna at the reader side, like the one that we are using. However, to mitigate the orientation mismatch problem, we have to employ more reading antennas around the tag interrogation zone.The previously described setup shown in The theoretical calculation of the noise floor of this setup is about It is also clear from In this paper, the major limitations of the FC chipless RFID tags are theoretically and practically investigated. The various tag designs which have been employed in this study are summarized in


When performing fault diagnosis tasks on bearings, the change of any bearing’s rotation speed will cause the frequency spectrum of bearing fault characteristics to be blurred. This makes it difficult to extract stable fault features based on manual or intelligent methods, resulting in a decrease in diagnostic accuracy. In this paper, a two-stage, intelligent fault diagnosis method  is proposed to deal with the problem of fault diagnosis under variable speed conditions. Firstly, the order tracking algorithm is used to resample the monitoring data obtained under different rotation speeds. Then, the one-dimensional convolutional neural network is adopted to extract features of the fault data. Finally, the fault type of collected data can be obtained by fully connected networks based on the features extracted. In the time domain, while the proposed algorithm only relies on the fault data collected under one speed as the training dataset, it is capable of doing fault diagnosis under different speed conditions. In the condition with the largest difference in speed with each dataset, the accuracy of the proposed method is higher than the baseline methods by 0.54% and 11.00%—on CWRU dataset and our own dataset respectively. The results show that the proposed method performs well in dealing with the fault diagnosis under the condition of variable speeds. With the development of science and technology, mechanical equipment is becoming more and more automatic and intelligent. As the key parts of mechanical equipment, rotating mechanical parts such as bearings and lead screws play an important role in the overall performance of the equipment . When thBearing fault diagnosis is a hot research field of mechanical condition monitoring. The extraction of monitoring signals’ features and pattern classification are the core steps of bearing fault diagnosis. Among various kinds of monitoring signals, the vibration signal, which has the advantages of being easy to monitor and rich in information, is widely used in the field of mechanical condition monitoring. When a certain part of the bearing fails (such as cracking of the rolling body and fatigue pitting corrosion of the inner ring or outer ring rolling), the bearings will produce periodic additional vibrations. The frequency of the additional vibration has a certain relationship with the bearing speed (Equations (2)–(5)), which is called the fault characteristic frequency. When transforming the vibration signal to the frequency domain, the signal components with the fault characteristic frequency will have a large amplitude. By identifying the frequency components of the original vibration signal, we can identify where the bearing failed.For the bearing fault diagnosis based on the vibration signal, the common feature extraction methods based on classical signal processing methods mainly include the Hilbert–Huang transform (HHT), the wavelet transform, empirical mode decomposition and methods based on largest Lyapunov. V.K. Rai et al.  adopted In recent years, the intelligent fault diagnosis methods based on machine learning and deep learning have achieved excellent results in the field of bearing fault diagnosis. P. Konar et al.  successfDeep learning methods such as convolutional neural network can automatically extract the high dimensional and low dimensional information in the original vibration signal. After network training, fault-related feature information in the original vibration signals can be effectively extracted and enhanced, and then the vibration signal can be classified. In our previous work , a one-dCompared with the benign situation that the bearing rotates at constant speed, this paper addresses a much more challenging problem where the bearing has variable speed, which directly leads to changes in the distribution of vibration signal, and hence makes it more difficult to diagnose. This challenge has been widely recognized in the bearing fault diagnosis community and still remains an open problem.The methods based on time-frequency domain analysis  and tranTo sum up, the methods of bearing fault diagnosis can be divided into four categories: methods based on classical signal processing algorithms in time domain/frequency domain/time-frequency domain analysis, methods based on traditional machine learning, methods based on deep learning and methods based on transfer learning . These mThis paper proposes a novel, intelligent fault diagnosis method for bearing fault diagnosis under variable speed conditions. Firstly, the order tracking algorithm is adopted for speed normalization of fault data under variable speed conditions, and then the one-dimensional convolutional neural network is used to extract the fault feature vectors and classify the fault data automatically. The proposed method takes advantage of the order tracking and deep convolutional neural network; the former resamples the fault data collected at variable speed; the latter extracts the characteristics of the resampled data and classifies the resampled data automatically. By using different data processing methods at different stages, the migration diagnosis from the fault data collected at a certain speed to the fault data collected at other speeds is finally realized.The contributions of this paper are as follows: Firstly, the proposed method is based on the convolutional neural network structure, and we develop the 2D-CNN into a 1D-CNN. The proposed 1D-CNN can adaptively extract the features of the monitoring data. This avoids the complex operations of manually designing and extracting the features of the fault data. Secondly, the proposed method has the least decrease in accuracy compared with the comparative methods dealing with the monitoring data collected at variable speeds. As OT-1DCNN adopts the order tracking algorithm to preprocess the original vibration signal. It can fundamentally solve the problem of changing the frequency spectrum characteristics of the fault data caused by variable speed conditions. Finally, the proposed method reduces the requirements for the completeness of the training datasets. The method only needs the data collected at just one speed, as the training dataset and the data with different distributions collected at other speeds can be classified at the same time. Additionally, the network does not need to be retrained. Differently from the intelligent diagnosis methods, the proposed network neither includes the domain adaptive network, nor needs to design and extract the distribution difference metric between different domain data. The structure and training process of the neural network are very simple.The rest of this paper is organized as follows: In As the most effective method to deal with the fault diagnosis under the condition of variable speeds ,20,21, tIn 2006, Saavedra P.N. ,23. The Hardware order tracking technology faces the difficulties of complex equipment and high testing costs in practical applications . BossleyTacholess order tracking is suitable for cases where the instantaneous speeds are difficult to obtain. When limited by the structure space and hardware cost of the equipment, there may be no speed sensors in the monitored equipment, so the speed information cannot be obtained directly. The tacholess order tracking method attempts to extract the speed signals directly from the vibration signals by some methods, and resamples the vibration signals in the angle domain according to the extracted instantaneous speed signals ,29,30. AVold–Kalman order tracking focuses on how to extract the signal components of each order from the original vibration signals, and then analyzes the time domain waveform of each order component ,32,33,34As can be seen from the above literature review, the order tracking algorithm is a powerful tool to deal with the problem of fault diagnosis under variable speed conditions. It can essentially overcome the influence of variable speed conditions on the distribution of fault data.In recent years, with the development of deep learning technology, the fault diagnosis algorithms based on neural networks have been used to solve the migration diagnosis problem under the condition of variable speeds. Viet Tra et al.  adopted In order to solve the problem of fault diagnosis for heterogeneous data collected under variable working conditions and variable equipment, the transfer learning method was introduced into the field of fault diagnosis. Kun X et al.  proposedThe above intelligent fault diagnosis methods based on deep learning have achieved certain success in dealing with the problem of fault diagnosis at variable speeds. However, their training data sets all need to contain the fault data collected at two or more speeds, which significantly increases the difficulty and cost of making the training dataset. Few intelligent fault diagnosis methods based on deep learning only use the training datasets collected just under a single rotating speed condition. This is the significant disadvantage of existing intelligent fault diagnosis algorithms.As is mentioned above, order tracking is superior in the ability to map the unstable time domain signal to the angular. It can essentially overcome the impact of variable speed operating conditions. For the monitored one-dimensional vibration signal, the proposed 1-DCNN convolutional neural network uses a one-dimensional wide convolution kernels (convolution kernel size is 64) in the first convolution layer. With the wide convolution kernels, the first layer in the network can obtain the frequency domain information in the signals. The proposed network uses the small convolution kernels in the subsequent layers to obtain more detailed features. 1-DCNN has the ability to automatically extract the weak fault features from the vibration data. Therefore, the combination of these two methods might be a robust approach.This paper proposes a two-stage, intelligent fault diagnosis algorithm to deal with the problem of fault diagnosis under variable speed conditions. Differently from the current fault diagnosis methods for variable speed working conditions, the proposed algorithm reduces the requirements on the data set. It only relies on fault data collected at one speed to train the network. After training, the proposed network has the ability to classify the resampled data collected at other speeds. In detail, the proposed algorithm firstly uses the order tracking algorithm to resample the original vibration signals collected at other speeds. After that, the resampled signals are obtained. Then, the resampled signals are sent to the pre-trained network. Finally, we can get the classification results of the fault data. The proposed method adopts the order tracking algorithm and a deep convolutional neural network in different processing stages, relies on the fault data collected at one speed as the training dataset and realizes the migration fault diagnosis of the fault data obtained under the other speed conditions. As a whole, the proposed algorithm finally uses the intelligent migration fault diagnosis from the fault data at a single speed to judge the fault data collected at other speeds. The flow chart of the proposed two-stage method is shown in The proposed two-stage, intelligent fault diagnosis algorithm not only adopts the order tracking method to deal with the variable speed conditions, but also has the ability to extract the feature vectors of the fault data automatically. In the time domain, the proposed algorithm only relies on the fault data collected at one speed as the training dataset, and realizes the migration fault diagnosis of the fault data obtained under the other speed conditions.O represents the order of fault; In the field of bearing fault diagnosis, the order is defined as the ratio of the fault characteristic frequency to the bearing speed . It can For rolling bearings, the common failure types include outer ring failure, inner ring failure, rolling element failure and cage failure. The fault characteristic frequencies of various fault types are expressed as follows:It can be seen from Equations (2)–(5) that when the structural parameters of the bearing are fixed, the frequency of each type of fault is linearly related to the frequency of rotation. When the speed of the bearing changes, the characteristic frequency of the bearing fault will also change.Correspondingly, we can get the order of various faults as follows:It can be seen from Equations (6)–(9) that when the structural parameters of the bearing are fixed, the characteristic orders of the bearing faults are also fixed. The characteristic orders of the bearing faults do not change along with the variable speeds. This characteristic of fault feature orders provides strong theoretical support to deal with the problem of fault diagnosis under variable speed conditions.In actual industrial scenarios, the bearing has many working conditions that are fixed at several certain speeds. For such cases, the implementation flow of the order tracking algorithm is shown in the The detailed steps of the order tracking algorithm are described as follows:Monitor the fault response of the monitored bearing under different speeds; obtain the fault response data Determine the reference speed The original sampling frequency at the reference speed is the basic sampling frequency for resampling, which is calculated as follows:Calculate the resampling frequency Plan the resampling time p-th resampling point of fragment p-th resampling point; j-th and (j + 1)-th data of the j-th and (j + 1)-th data of the Determine the interpolation algorithm. When the resampling points calculated in the previous step fall between the original two discrete data points, the values of the multi-sampling data points need to be interpolated. Commonly used interpolation methods are linear interpolation, Newton interpolation and Lagrange interpolation. In order to improve the calculation efficiency, this article uses linear interpolation method. The formula is as follows:After acquiring the resampled data points The convolution networks used in the field of fault diagnosis are mostly based on the two-dimensional convolutional neural network structures. In our previous research , we intrFrom the above table, we can find that the network with four convolutional layers and two fully connected layers achieves the highest accuracy. Additionally, the results show that the convolutional layers play a more important role than the fully connected layers. The networks with the same number of the convolutional layers tend to have the similar results. Thus, a one-dimensional convolutional neural network with convolutional layers and two fully connected layers is adopted for the fault diagnosis tasks. The structure and parameters of the network are shown as As shown in q(x) denote the estimated distribution and p(x) denote the target distribution; the function of the cross-entropy is shown as:The structure of the proposed 1D-CNN is shown as −6 and the number of iterations is 1000. When training the network, first of all, the data enhancement method is applied in the training dataset. The training data and testing data used in the experiments were one-dimensional vibration signals. Under a single working condition, the length of the original monitoring signals for each health state was set to N, the length of each input data of the network was 2048 and we sampled the training data at intervals of 10 data points in the original vibration data sequence. We got (N-2048)/10 + 1 samples from each original vibration data sequence. Secondly, batch normalization operation is applied in each convolutional layer. Since the network we use is 1D-CNN, the BatchNorm1d function is adopted to do this. Finally, in the fully connected layers, we adopt dropout operation and the rate of dropout is set to 0.5.The stochastic gradient descent (SGD) method is used as the optimizer, the batch size is set to 40, the learning rate is set to 1.0 × 10In this study, two different bearing fault datasets were used to verify the effectiveness of the proposed algorithm under variable speed conditions. Firstly, in order to verify the superiority of the proposed algorithm, we used Case Western Reserve Bearing Database  to conduThe Case Western Reserve University Bearing Data Center Website privates the ball bearing test data for normal and faulty bearings. All the acceleration data were collected in the experiments conducted using a 2 hp Reliance Electric motor. The vibration data were recorded for motor loads of 0 to 3 horsepower and the motor speeds of 1797 to 1730 RPM. The fault data were divided into four types: normal data, inner ring fault data, outer ring fault data and rolling element fault data. The device is shown as In this study, we made four datasets, A, B, C and D, to conduct the experiment. In each dataset, there are training data and testing data. The training data in each dataset only contain the data of each health state collected under one speed. The testing data contain the data of each health state collected under four speeds. The comparative experiments directly used the deep convolutional neural network to verify the migration diagnosis effect between different rotation speed states, without using the order tracking algorithm to preprocess the original data. The descriptions of the bearing fault datasets are as shown in In each dataset, we used the speed of the training data as the basic rotation speed; then calculated the resampling frequency of the original vibration data under each speed; and finally resampled the original data according to the resample frequency of each speed. In each health state under each speed, we took 3000 samples and the length of each sample was 2048. In each dataset, the training dataset contains four types of health state data  under one speed; thus, the total number of the training data is 3000 × 4 = 12,000. The testing dataset in each dataset contains the resampled data with all the types of health sate under each rotation speed; thus, the total number of testing data in each dataset was 12,000 and the length of each data sample was also 2048.After getting all the training data and testing data in each dataset, we can carried out the experiments. Firstly, we trained the deep convolutional neural network with training data, the input the test data under each speed to the trained network and got the migration classification accuracy from the train data to the test data at 1730, 1750, 1772 and 1797 RPM respectively. The detailed data processing flow is as shown in In order to prove the effectiveness of the order tracking algorithm, this study used Case Western Reserve University Bearing Data Set for experiments. Motor bearings were seeded with faults using electro-discharge machining (EDM). Faults ranging from 0.007 inches in diameter to 0.040 inches in diameter were introduced separately at the inner raceway, rolling element  and outer raceway. Faulted bearings were reinstalled into the test motor and vibration data were recorded for motor loads of 0 to 3 horsepower (motor speeds of 1797 to 1720 RPM). In the above data, we selected health status data, inner ring fault data, outer ring fault data and ball fault data at four speeds for order tracking and resampling. The experimental results are shown in the following figure.The purpose of order tracking is to overcome the ambiguity of the fault characteristic spectrum, which is caused by the speed change. We set 1730 rpm as the base speed, and the corresponding vibration data at the 1730 speed as the basis sampling frequency. The order tracking algorithm resampled the fault data at 1797 speed, and the Fourier transform was performed on the original data before resampling and the fault data after resampling. The results of Fourier transform are shown as In In dataset A, we took the collected data with 1730 rpm as the training data to train the DCNN. With the trained network, we classified the resampled fault data with 1730, 1750, 1772 and 1797 rpm. The classification accuracy of the network’s fault data under each speed state can reflect the proposed algorithm’s ability to diagnose fault data under variable speed conditions. The experiments were implemented using the Pytorch framework in Pycharm Community 2019.1. The classification results with each dataset are shown as From To verify the superiority of OT-1DCNN, we conducted the comparative experiments with CWRU data. In the comparative experiments, the OT-1DCNN, DCNN, AlexNet and VGGNet were adopted on dataset A, dataset B and dataset C respectively. In order to keep the consistency of the input data, we modified the structures of the DCNN, AlexNet and VGGNet, making them suitable for processing the one-dimensional vibration signals. The number of the four networks’ input layer’s nodes was 2048, which is the same as OT-1DCNN. Among them, DCNN contained 4 convolutional layers and 2 fully connected layers; AlexNet contained 5 convolutional layers and 3 fully connected layers; VGGNet contained 6 convolutional layers and 2 fully connected layers. The results of comparative experiments are shown in With dataset A, the accuracies of OT-1DCNN, DCNN, AlexNet and VGGNet were 0.9969, 0.9893, 0.9826 and 0.9998 respectively. VGGNet got the highest accuracy, which was higher than OT-1DCNN by just 0.29%. With dataset B, the accuracies were 0.9976, 0.9714, 0.9733 and 0.9927 respectively. With dataset C, the accuracies were 0.9895, 0.9492, 0.9519 and 0.9841 respectively. With dataset B and dataset C, OT-1DCNN got the highest accuracy.To further verify the effectiveness of the proposed algorithm, we carried out further experiments on our own bearing fault platform. The self-made device is shown as On this experimental platform, we only used the fault data collected at 900 RPM as the training dataset, and the fault data collected at 1020, 1140 and 1260 RPM as the test datasets. The fault data under each speed state included three states: health state, inner ring fault and outer ring fault. There were 3000 samples in each state of health in each speed state, and each sample contained 2048 vibration data points. The datasets used in the test were as shown in In this experiment, we used the same data processing process as the fault data on the Case Western Reserve bearing database. For the fault data set containing only three types, we adjusted the number of neurons in the last layer to three. The results of the experiment are shown as From To further verify the superiority of OT-1DCNN, we conducted further experiments based on the data collected on the self-made test device. Compared with CWRU dataset, the speed difference between the training dataset and the testing dataset is greater. This can more clearly prove the migration diagnosis ability of the OT-1DCNN. The structures of the four networks used in this experiment were exactly the same as those in experiment A. The results of comparative experiments with the self-made dataset are shown as From The proposed OT-1DCNN method can effectively deal with the problem of decreased fault diagnosis accuracy, which is caused by variable speed conditions. The proposed algorithm firstly resamples the original signals with order tracking algorithm. Then a one-dimensional convolutional neural network is used to adaptively extract the features of the fault signals and classify the data automatically. In the network training stage, only the fault data obtained at one speed is adopted to train the network. The trained network performed well in dealing with the fault data collected at other speeds, even though the testing data had a different distribution from the training data. Our results in the experiments show the OT-1DCNN algorithm performs better than the comparative methods.In the proposed OT-1DCNN algorithm, it was proven in the experiments that the order tracking algorithm can improve the stability of the frequency spectrum distribution of the fault characteristic signal in variable speeds condition. It can transform the vibration signal from time domain to angle domain by resampling the original signals. For the resampling signals, the spectrum characteristics will not change along with the variable speeds. In this case, the problem of an unstable signal spectrum will be overcome. Additionally, the convolutional neural network has the ability to adaptively extract the effective information hidden in the original monitoring signal, avoiding the complex process of feature design and the extraction.From the perspective of math principle, the proposed OT-1DCNN algorithm can completely solve the problem of decreased diagnostic accuracy of the network, which is caused by variable speeds. However, when the discrepancy of speeds between training data and testing data gets bigger, the accuracy of the network still decreases to a certain extent. The authors will investigate these issues in the future works.This paper proposes a two-stage bearing fault diagnosis algorithm to realize the diagnosis of bearing fault data under different speed conditions. The algorithm effectively combines the order tracking algorithm with the one-dimensional convolutional neural network. The order tracking algorithm is good at dealing with the problem of an unstable signal spectrum in variable speed conditions. The one-dimensional convolutional neural network can adaptively extract the features of the fault signals and classify the data automatically. The proposed OT-1DCNN algorithm adopts these methods at different data processing stages to make full use of the advantages of them. By doing this, the proposed method can reduce the dependence on the completeness of the training datasets. The algorithm only uses the fault data collected under one speed as the training dataset, and realizes the migration diagnosis of the fault data collected at other speed states. This study used the Case Western Reserve bearing database and our own bearing failure data experimental platform to obtain experimental data for experimental verification. In the condition with the largest difference in speed with each dataset, the accuracy of the proposed method was higher than for the comparative methods by 0.54% with CWRU dataset and by 11.00% with our own dataset respectively. The experimental results show that the proposed algorithm can significantly improve the DCNN migration diagnosis effect under variable speed conditions in the time domain with the same training datasets. In the experiment, we found that the migration diagnosis accuracy of the network will decrease as the speed difference between the training set and the test set increases. Future research work will continue to explore the reasons for the decline in network classification accuracy.


A plantigrade foot with a large robust calcaneus is regarded as a distinctive morphological feature of the human foot; it is presumably the result of adaptation for habitual bipedal locomotion. The foot of the Japanese macaque, on the other hand, does not have such a feature, which hampers it from making foot–ground contact at the heel during bipedal locomotion. Understanding how this morphological difference functionally affects the generation of bipedal locomotion is crucial for elucidating the evolution of human bipedalism. In this study, we constructed a forward dynamic simulation of bipedal locomotion in the Japanese macaque based on a neuromusculoskeletal model to evaluate how virtual manipulation of the foot structure from digitigrade to plantigrade affects the kinematics, dynamics, and energetics of bipedal locomotion in a nonhuman primate whose musculoskeletal anatomy is not adapted to bipedalism. The normal bipedal locomotion generated was in good agreement with that of actual Japanese macaques. If, as in human walking, the foot morphology was altered to allow heel contact, the vertical ground reaction force profile became double-peaked and the cost of transport decreased. These results suggest that evolutionary changes in the foot structure were important for the acquisition of human-like efficient bipedal locomotion. Oku, Ide and Ogihara use forward dynamic simulation to virtually manipulate the foot posture of the Japanese macaque from a digitigrade to plantigrade posture for bipedal locomotion. This postural shift results in greater energetic economy despite the macaque not having anatomy adapted for bipedal movement. Structural changes in the foot are likely a key component of the acquisition of human-like bipedal locomotion. Furthermore, nonhuman primates do not generally exhibit the characteristic double-peaked vertical ground reaction force (GRF) profile seen in humans (see Schmitt2 for a review). Some chimpanzees are reportedly capable of generating double-peaked vertical GRF3, but the force profile is not the clear two-peak pattern of humans. Owing to these kinematic and kinetic differences, phase and/or amplitude of fluctuation of the body’s center of mass (COM) and hence mutual transfer of potential and kinetic energy during bipedal locomotion are somewhat different between humans and nonhuman primates, resulting in lower energy recovery from exchange of potential and kinetic energy during bipedal locomotion in nonhuman primates than in humans7.Nonhuman primates such as chimpanzees and macaques generally have the ability to walk bipedally. However, bipedal locomotion of an inherently quadrupedal primate is different from that observed in humans. For example, the hip and knee joints are more flexed throughout the gait cycle8. The structure of the human foot is different from those of nonhuman primates; this is presumably the result of morphological adaptation for the generation of stable and efficient bipedal locomotion13. For example, the opposability of the hallux, and hence, the prehensile capability of the foot in nonhuman primates, is absent in the human foot. Furthermore, the human foot uniquely possesses a longitudinal arch with an enlarged, robust calcaneus, the tuberosity of which points posteriorly and inferiorly, allowing prominent heel strike during plantigrade gait in humans17. However, the primate foot does not possess such a longitudinal arch, and its calcaneal tuberosity points posteriorly and superiorly  joint must be dorsiflexed before touch down and hence the flexor digitorum longus is stretched at the time of foot contact20. Therefore, macaques do not walk bipedally with heel contact. African great apes have plantigrade feet with its calcaneal tuberosity directed posteriorly without being inclined substantially and hence can walk with a heel strike24, but the heel and midfoot often contact the ground simultaneously24, and the calcaneus is not as derived as that in humans. Therefore, a robust calcaneus is considered to be one of the fundamental morphological adaptations for the acquisition of habitual bipedal locomotion in humans.Such differences in bipedal walking between humans and nonhuman primates exist because of structural differences in the musculoskeletal system. Among these differences, those of the foot, along with the pelvis and femur, seem to be important, as it is the most distal segment of the body that directly interacts with the ground25 experimentally demonstrated that human walking with plantigrade feet required less energy than that with digitigrade feet because of the reduced energy loss during collision between the foot and the ground, the increased utilization of the inverted pendulum mechanism26, and a reduced ankle joint moment. Webber and Raichlen27 studied human walking with foot-ground contact with the balls of the foot initially with heel contact occurring later in the step and noted that the decrease in the energetic cost occurred in human walking with heel contact because of the increase in the effective limb length owing to the larger anterior translation of the center of pressure (COP). These findings suggested the possible functional significance of the evolution of the plantigrade foot to allow bipedal locomotion with heel contact, as observed in humans. However, in those studies, increased energy consumption with forefoot contact may have been observed, possibly because the human musculoskeletal system, in addition to the motor control system, has been adapted to heel but not to forefoot strike bipedal locomotion over the course of human evolution. How the evolutionary changes in the structure of the foot and the way it interacts with the ground affect the mechanics and energetics of bipedal locomotion in early hominins whose musculoskeletal structure differed from humans remains unclear.Recently, it was hypothesized that bipedal walking with plantigrade foot and heel contact is energetically more economical than that with digitigrade foot and forefoot contact. For example, Cunningham et al.32. Chimpanzees were commonly thought to be the most appropriate living proxies for the last common ancestor of both humans and chimpanzees. However, chimpanzees are well specialized to suspensory-inclined locomotion and knuckle-walking in terms of musculoskeletal anatomy35. After the discovery of Ardipithecus, it was hypothesized that, unlike modern apes, the last common ancestor was a relatively large-bodied but non-suspensory arboreal clamberer albeit whose trunk and aspects of their limbs were more derived than that in general pronograde quadrupeds, such as early and middle Miocene African apes36 [but see Pilbeam and Lieberman37 for alternative arguments]. Therefore, utilizing a generalized quadrupedal primate such as the macaque that is less-specialized in terms of locomotor anatomy35 as a living model of the hypothetical protohominids is of increasing importance to clarifying and reconstructing the evolution of bipedal locomotion in the early hominins.Our group has been investigating bipedal locomotion in Japanese macaques as a way to achieve a better understanding of the evolution of human bipedalismIf the feet of bipedal Japanese macaques could somehow be manipulated to that of humans to allow for bipedal gait, the possible changes that might occur in bipedal locomotion could be observed, which would offer an opportunity to investigate the evolutionary advantage of human foot morphology in hypothetical protohominids. However, we certainly cannot replace the macaque foot with a human foot in vivo to evaluate the effect of changes in foot morphology on the mechanics and energetics of bipedal locomotion. To investigate possible changes in bipedal locomotion resulting from alterations in the musculoskeletal system, an alternative method is necessary.57. This predictive simulation technique has also been conducted in the field of physical anthropology to help understand the evolution of human bipedal locomotion61. A forward dynamic simulation of bipedal walking in the Japanese macaque could enable changes in the mechanics and energetics of bipedal walking resulting from virtual alteration of the musculoskeletal system to be predicted. Therefore, in the present study, we constructed a muscle-driven forward dynamic simulation of bipedal locomotion in the Japanese macaque based on a two-dimensional (2D) neuromusculoskeletal model and evaluated how virtual manipulation of foot morphology affects the kinematics, dynamics, and energetics of bipedal locomotion. Specifically, we investigated how the alteration of the foot from digitigrade to plantigrade by the inferior translation of the calcaneal tuberosity, which allows heel strike bipedal locomotion, affects the kinematics, dynamics, and energetics of bipedal locomotion in the Japanese macaque using computer simulation.A forward dynamic musculoskeletal simulation is a computational technique used to calculate muscle-driven skeletal motions by integrating differential equations that define the dynamics of a musculoskeletal system. Many musculoskeletal forward dynamic simulations of bipedal walking have been conducted to clarify the biomechanics and motor control of human locomotion62 is shown in Fig. 62 is also shown in Fig. 31. The muscle force profiles  element was observed in the iliopsoas muscle. The macaque is inherently a quadrupedal animal, and hip flexor muscle  restricts hip-joint extension. When the macaque walks bipedally, the hip joint must be more extended than usual and the PE element contributes significantly. The PE element was also largely contributed in the gastrocnemius and flexor digitrum longus muscles during dorsiflexion of the ankle and MP joints. The estimated gross mass-specific metabolic cost of transport was 14.5 J/(kg m), whereas that estimated based on measured CO2 production rates29 was ~15 J/(kg m)5, indicating that the cost of transport was also reasonably well estimated. Therefore, our simulation framework successfully reproduced the basic kinematic and dynamic features of bipedal locomotion in the Japanese macaque, even though modeling of the musculoskeletal system was confined two-dimensionally. This simulation can be used to investigate predictively the effects of alterations in foot morphology on the kinematics, dynamics, and energetics of bipedal locomotion in the Japanese macaque.We firstly compared the simulation of walking in the original Japanese macaque model with the unaltered foot and experimentally obtained walking data for evaluation of the simulation. Stick diagrams of the simulated and experimentally obtained bipedal locomotion of the Japanese macaque are shown in Fig. les Fig.  were als27. In addition, the magnitudes of the breaking and propelling forces were substantially reduced if foot morphology was altered . The joint moment and muscle force profiles were generally similar between before and after the foot alteration, but notable differences were observed in the ankle moment and soleus muscle force; the maximum force generated by the soleus and hence the ankle moment was decreased as a result of the altered foot morphology. The change in the predicted gross metabolic cost of transport as the most posterior contact point of the foot corresponding to the calcaneal tuberosity was inferiorly translated is shown in Fig. 26, of the bipedal locomotion generated before and after the alteration of foot morphology was 20.0% and 27.4%, respectively, indicating that the inverted pendulum mechanism was better utilized when foot morphology was altered.A stick diagram of the generated bipedal locomotion with altered foot morphology  compared with that of the intact foot is shown in Fig. 19 have indicated that the ankle joint is more plantarflexed and that the foot segment is more vertically oriented at the time of toe-off in Japanese macaques than in humans. Therefore, the joint angles in the simulated bipedal locomotion were actually changed toward those observed in human and chimpanzee bipedal locomotion owing to altered foot morphology.If the foot of the Japanese macaque is changed to allow heel contact like a human foot, our simulation predicted that the knee was more extended in the stance phase, and that the ankle and MP joints were less plantarflexed and dorsiflexed, respectively, in the late stance phase. Kinematic comparisons of bipedal locomotion between Japanese macaques and humansWe also demonstrated that the metabolic cost of transport of bipedal locomotion decreased if foot morphology was altered. The proximate cause of this decrease is the reduction in the soleus muscle force Fig. . In the 2, and it is known to be functionally related to the efficiency of gait64. Because the force profile has two peaks in human walking, the net vertical force exerted to the body’s COM is greatest during the double-support phase and lowest during the mid-stance phase, which results in the vertical oscillation of the COM between a high point during the mid-stance phase and a low point during the double-support phase. Since horizontal velocity is lowest at the mid-stance phase and highest at the double-support phase, potential and kinetic energy fluctuate out of phase with almost equal amplitude in human bipedal walking like a simple pendulum. This out-of-phase fluctuation of the two types mechanical energy is the fundamental mechanism for saving energy in human walking65. The fact that the generated bipedal locomotion exhibited, although moderately, a double-peaked vertical GRF profile because of the alteration of foot morphology is therefore linked to the decrease in the cost of transport. Nevertheless, the vertical GRF of the altered foot model was not the clear two-peaked pattern of humans, but was more like that occasionally observed in chimpanzee bipedal walking3. Chimpanzees have a plantigrade foot and can make a heel contact during bipedal walking, but the heel and midfoot most often contact the ground simultaneously because the calcaneus is not as derived as that in humans. This fact possibly corroborates with the present result indicating the plantigrade foot leads to the emergence of the double-humped force curve in non-human primate bipedal locomotion.The change in foot morphology also evoked a change in GRF profile and whole-body mechanics during bipedal locomotion. Although the second peak was not as prominent as that observed in human walking, the double-peaked vertical GRF profile emerged in the altered foot model. The double-peaked vertical GRF profile is one of the most distinctive characteristics of human bipedal walking because nonhuman primates do not generally exhibit this force pattern66. The peak vertical GRF profile decreases and the duration of the stance phase is prolonged if the leg is relatively compliant. This is the reason why nonhuman primates generally adopt so-called grounded running, defined as a gait utilizing spring-like running mechanics, even though the duty factor is >0.5 when moving on two legs32. In humans, however, grounded running is not generally observed. Humans utilize pendular mechanics if the duty factor is >0.5 and spring-like bounce mechanics if it is <0.5, and the transition from walking to running is discontinuous67. Therefore, the acquisition of walking gait utilizing the pendular mechanism by stiffening the stance leg is one of the critical transitions in the course of human evolution. The present predictive simulation implies that the evolution of the foot, particularly the acquisition of the human-like plantigrade foot possibly due to the evolutionary change of the calcaneus may facilitate generation of the two-peaked vertical GRF profile and improve the energetic efficiency of bipedal locomotion via the inverted pendulum mechanism, despite the fact that th`e other parts of the body are not yet specialized to the generation of bipedal locomotion. Improved locomotor economy is a strong evolutionary advantage for foraging and reproduction. The evolution of the foot could be a fundamental initial trigger for the evolution toward the acquisition of human-like bipedal locomotion. It must be noted that digitigrade terrestrial birds show a two-peaked GRF profile during bipedal walking70, and so do humans walking on toes71, indicating that plantigrade gait with human-like heel contact is not a necessary condition for the double-humped force curve. However, the present study indicated that the alteration of the foot from digitigrade to plantigrade foot could be one possible condition or scenario leading to the evolution of human-like bipedal walking for hypothetical hominids.The emergence of the double-peaked vertical GRF profile could be attributable to the fact that the forward translation of the COP started more posteriorly from the rear foot in the altered foot model. Because the GRF vector passed nearer to the ankle joint, the leg stiffness increased in the early stance phase in the altered foot model. The leg stiffness also increased in the late stance phase because the knee was more extended due to the fact that the whole-body kinematics and hence the COM movement was altered and the shank vaulted over the foot more slowly Fig. . A stiffIn human walking, the second force hump of the vertical GRF profile is generated due to activations of plantarflexor muscles such soleus and gastrocnemius, but in the macaque model, the forces generated by these triceps surae muscles is not as prominent as that in humans, resulting in the absence of the prominent second force hump. Therefore, in the macaque model, the second peak was generated in a different manner from human walking. However, this change observed in the macaque model also contributes to the energetic efficiency of bipedal gait, and the improved locomotor economy certainly is an evolutionary advantage.73 accompanied by the fossilized footprints found in Laetoli75 suggest that Australopithecus afarensis walked with a prominent heel strike. Our simulation results imply that the vertical GRF profile of bipedal locomotion in A. afarensis exhibited the characteristic double-peaked vertical GRF profile, allowing utilization of the inverted pendulum mechanism at least higher than that observed in macaque bipedal locomotion with a single-peaked vertical GRF profile. The same is probably expected for A. sediba, because of its plantigrade foot, even though its calcaneus was relatively slender76. It must be noted, however, that although the bipedal locomotion generated in the present study was altered toward human-like bipedal locomotion, it is still essentially a bent-hip, bent-knee gait that is actually quite different from human bipedal locomotion, and the GRF profile is not the clear two-peaked pattern of humans. The %recovery of the generated bipedal locomotion is also relatively low (27.4%) and the value is within the range reported for chimpanzees (2–45%7). This fact could indicate that other anatomical constraints such as restricted lumbar spine mobility77, different gluteal morphology79 and/or restricted hip joint mobility owing to hip flexor muscles31 might also need to be modified for hypothetical protohominids to acquire human-like bipedal walking fully with improved utilization of the inverted pendulum mechanism. In addition, feet without a human-like longitudinal arch and prominent plantar aponeurosis82 should also be altered for effective propulsive force generation as observed in human walking. Further, the evolution of a larger body could be another possible prerequisite for the acquisition of bipedal walking with full utilization of the inverted pendulum mechanism because larger animals tend to take a more extended leg posture to decrease muscular forces by increasing muscle mechanical advantage83. The contributions of such anatomical factors to the acquisition of truly human-like bipedal locomotion should be investigated in future studies using the present predictive model.A relatively human-like calcaneus with a large, robust tuberosity and plantarly located lateral plantar process85, including Japanese macaques19. However, the mobility of the midfoot is much lower than that of other joints, which suggests that the absence of the midfoot joint in our model had only a minor effect on the results of the present study. Another limitation was that we used simple 2D models of the musculoskeletal system and muscle force production. Major segmental movements during bipedal locomotion are confined to the sagittal plane, even in the Japanese macaque. Therefore, this was assumed to have only a minor impact on the predicted differences in the global body mechanics of bipedal locomotion. It must be noted, however, that omission of the force-length and force-velocity relationships of the muscles could have considerable effects on muscle gearing ratio changes86. In addition, although the muscle PE element was incorporated in the present study, no muscle series elastic elements, i.e., tendons, were included. As the simulated bipedal locomotion was not fast, the effect of the absence of tendons was thought to be small; however, the incorporation of a musculotendon model with correct identification of its mechanical parameters should also be investigated in future studies. Furthermore, the choice of 36 mm inferior translation of the calcaneal tuberosity as a human-like heel height was arbitrary and could have had important effects on the result of the current study. Lastly, although the simulated results generally agreed with the measured data and captured the main features of bipedal gait in the Japanese macaque, the GRF profiles did not closely match each other, possibly due to the problem associated with modeling of foot-ground contact mechanics, one of most challenging problems in the field of computational walking simulation87. For example, instantaneous vertical force development right after the foot-ground contact in the simulation , thighs, shanks, and feet, which are represented by two parts—a tarsometatarsal and a phalangeal part—as shown in Fig. 62. Each joint was modeled as a hinge joint. The viscous property of each joint was modeled by a linear viscous element. The viscous coefficients of the hip, knee, and ankle joints were determined to be 0.109, 0.317, and 0.0943 Nms/rad, respectively, or one-tenth of the human values reported by Davy and Audu89 because the macaque was about one-tenth the mass of a human. The viscous coefficient of the MP joints was determined to be 0.01 Nms/rad, approximately one-tenth of that of the ankle joint. To prevent hyperextension of the knee joint, a nonlinear elastic element89 was attached:k1, k2, and k3 are the coefficients determined as 1, 30, and −0.23, respectively.We constructed a 2D musculoskeletal model of the bipedal Japanese macaque based on the anatomically based 3D whole-body musculoskeletal model88. In cases where the path of a muscle could not be described by a single line segment, an intermediary point was defined. These points were fixed to the corresponding bone coordinate systems. Thus, the moment arms of the muscles changed depending on the joint angles.In this study, we considered ten muscle groups classified according to disposition Fig. , Table 2m is the muscle number, mth muscle, 62  layer that generates oscillatory signals and a pattern formation (PF) layer that generates muscle activity patterns based on the phase signal from the RG layer96. Therefore, in the present study, a mathematical model of the CPG consisting of the RG and PF layers was constructed , T is the duration of the gait cycle, and K is a gain parameter. In this study, T and K were determined to be 0.747 s and 1, respectively, as in Ogihara et al.62. The PF layer then generated the activation pattern of each muscle represented by a combination of two Gaussian basis functions of the phase signal mth muscle represented by the sum of two Gaussian functions, γm ≤ 1), Animal locomotion, including that of primates, is generally accepted as being produced by a rhythm-generating neuronal network in the spinal cord known as the central pattern generator (CPG), with locomotion evoked by stimulus input from the mesencephalic locomotor region in the brain stemted Fig. . The RG 96. To take this into account, we reset the oscillator phase 49, since cutaneous afferents contribute strongly to phase resetting behaviors98.The RG layer in the CPG is known to modulate its basic rhythm by producing phase shifts and rhythm resetting based on sensory informationIn addition, we assumed a simple feedback control for postural control of the trunk segment by hip uniarticular muscles (the iliopsoas and gluteus medius) of the support leg as follows:J, given by the following:D; 5); 62; 100.To generate bipedal walking, an appropriate activation pattern must be determined for each of the ten muscles. In the present study, we used a genetic algorithm for tuning a total of 60 parameters defining the sequence of muscle activation patterns so as to minimize the following objective function www.ode.org) with Microsoft Visual Studio 2010 C++, and then we solved the equation of motion using the implicit Euler method with a time step of 0.1 ms. We solved the differential equations of the nervous system using the Runge–Kutta method with the same time interval.We constructed the musculoskeletal model of the Japanese macaque using the Open Dynamics Engine rigid body physics library  was translated inferiorly by 1 mm and the parameters were tuned to generate locomotion and minimize energy expenditure with the new foot morphology Fig. . This prFurther information on research design is available in the Description of Additional Supplementary FilesSupplementary Data 1Reporting Summary


Climate change has influenced a range of species across the globe. Yet, to state a noted decline in the abundance of a given species as a consequence of a specific environmental change, for instance, spatially explicit long-term data are a prerequisite. This study assessed the extent to which prolonged snow-free periods in autumn and spring have contributed to the decline of the willow grouse, the only forest grouse changing into a white winter plumage. Time-series data of willow grouse numbers from summer surveys across the study area were integrated with local data on weather (snow cover), mammalian predator abundance and hunting intensity. Modelling was conducted with a hierarchical Bayesian Poisson model, acknowledging year-, area- and location-specific variability. The results show that while willow grouse numbers had decreased continuously across the study landscapes, the decrease was accelerated at the sites where, and during the years when the preceding April was the most snow-free. This indicates a mismatch between the change into a white winter plumage and the presence of snow, turning the bird into an ill-camouflaged prey. The results thus also confirm past hypotheses where local declines of the species have been attributed to prolonged snow-free periods. Across our study area, autumns and springs have become more snow-free, and the trend has been predicted to continue. Thus, in addition to conservation actions, the future of a species such as the willow grouse is also dependent on its ability to adapt to the changed environmental conditions. Simultaneously, species and ecosystems are being affected by weather fluctuations within extreme values as well as by direct anthropogenic actions7. Even if the effects of normal weather anomalies, anthropogenic actions and climate change may be hard to disentangle, it is clear that they can exacerbate one another. Further, even when the mechanisms of species’ and ecosystem’s resilience towards environmental changes are well known, the impacts of abrupt changes in weather patterns may be too sudden for some species to adapt to. Concrete examples of such events are observable in the northern hemisphere where changing and diminishing snow covers have altered seasonal characteristics of entire landscapes8, and so affected the local flora and fauna10. The effect can be more serious the more dependent the species is on snow, and this seems to be the case with a boreal bird species that once was abundant all across Finland: the willow grouse (Lagopus lagopus).Trends in global climate change are already affecting species and ecosystems13. To a large extent, this latter, more widespread decline has been attributed to the draining and afforestation of peatlands  -widespread across Finland between the 1950s and the 1980s, affecting up to 80–90% of the peatlands in areas of Southern and Central Finland14. The drainage activities affected the reproductive output of all grouse species negatively15, but for the willow grouse the drainage has been attributed as one of the major drivers of its decline in southern parts of the country16.Finland hosts willow grouse in two distinct populations, occupying different habitats: the northern populations occur in the areas of northern Finland with practically no forest cover, while the southern populations occur solely in forested areas, where they are typically found close to open mires and bogs within heavily forested landscapes. From now on, the term ‘willow grouse’ refers to the non-tundra populations occurring within the forested landscapes. The numbers of the tundra population have been comparably stable compared to those of the forest populations, which in the south, saw heavy, apparently warming-induced declines already in the 1930s. These were followed by partial revivals, but since the 1960s, the populations across southern and central Finland have been declining rather continuously17. For the declining willow grouse, additional conservation measures have also been taken: the species has been restricted or completely banned from hunting in central and southern Finland since the early 2000s. Shortly before this, it was discussed18 that the future of the willow grouse seemed positive, as habitat quality was likely to stay at least at the same level . However, the same author also pointed out that the milder winters and the endured snow-free periods might pose a further threat, as was seen in the past, prior to the drainage activities. Indeed, when viewed today, the continuing decline of the willow grouse populations requires research on the extent to which the known decrease in snow covers in the boreal landscapes has affected it.Eventually, the loss of the natural mire habitats was seen as becoming too widespread, and since the 1990s, draining of new peatland areas has been virtually non-existent. In addition, campaigns to restore the peatland areas back to their original state have been conducted in growing numbers. Until 2013, some 20,000 hectares of drained peatlands have already been restored, with an additional 18,000 hectares in need19. To a strong degree, the changing of plumage is controlled by the amount of light, which means that the process is not in complete synchrony with possible changes in snow cover, and Finnish winters have seen decreased snow covers as autumns and springs have become warmer21. Therefore, the evolutionary response to snow could turn the willow grouse into an ill-camouflaged beacon against a dark ground – and as with the other forest grouse species, the main cause of willow grouse mortality, regardless of human hunting, is caused by predation by raptors, the goshawk (Accipiter gentilis) in particular24. Past studies have confirmed that a white willow grouse is further vulnerable to goshawk predation during autumns and especially springs27, but so far the potential declining effect of this phenomenon has neither been quantified nor assessed at population level. In this light, no conservation action can guarantee the survival of the forest willow grouse if, indeed, the decline from the past 20 years is attributed also to the more frequent snow-free autumns and springs. This is a highly topical question, since the boreal regions (including Finland) have warmed more rapidly than the other parts of the world with profound effects on snow covers28.Snow is an especially crucial factor as the willow grouse, unlike the other forest grouse species in Finland has a white winter plumage. Ideally, the plumage is changed in synchrony with the arrival of the permanent snow cover in autumn as well as its disappearance in spring, and it has been suggested that its main function in the boreal zone is to provide camouflageThis study combines 21 years of willow grouse census data with data on predator abundance, hunting and local data on daily snow depth measurements. The aim of the paper is to assess the extent to which prolonged snow-free periods in autumn and spring explain or contribute to the observed decline in willow grouse populations on the consecutive summer. The results are viewed in light of the recent predictions on how climate change may affect boreal winters and what this means for the future of the species, even with heavy conservation efforts.12. The summer counting is done in late-July or early-August, specifically to estimate the grouse numbers and the success of grouse breeding prior to deciding the length of, and possible restrictions to, the autumn´s grouse hunting season. The route is surveyed by a three-person team , who walk the route and mark the locations of every grouse observed along the way (inside a 60-meter-wide belt). The data thus consists of observations based on grouse adults and broods, separated by species. In the winter survey, all animal tracks crossing the survey route are counted, and based on this, an abundance index is derived: number of crossings/24 h/10 km. For determining such an index, the survey is conducted with strict protocols: either the survey is made 1–2 days after a fresh snowfall, or alternatively, the route can be surveyed twice: all animal tracks are marked during the first survey, after which the second, proper survey and the counting of new tracks is conducted 1–2 days later. The wildlife triangle census was launched in 1989, and the data have been of crucial importance for a variety of wildlife- and grouse-related studies31. However, based on expert’s knowledge we only use data from the year 1996 onwards due to the data collection methods and protocols not being fully harmonized during the first survey years.Data on willow grouse abundance were provided by the Natural Resources Institute Finland (LUKE). The data were obtained from the Wildlife Triangle Censuses, a wildlife population monitoring program that has been active in Finland since 1989. Altogether, there are over 1,500 monitoring triangles located across Finland, and around 900 of these are surveyed annually. The ‘triangle’ itself is an equilateral triangle with each side measuring 4 km, adding up to form a 12-km long permanent inventory route. The route is checked twice a year (winter and summer), with the main purpose of providing information on the status of wildlife populations(Martes martes) and red fox (Vulpes vulpes), opportunistic yet potential predators of willow grouse, and the summer data were used to gain information on willow grouse abundance. Willow grouse chicks were not included in the analysis, as their mortality would not be affected by autumn and spring-time snow conditions; they are born in June after which their mortality is primarily determined by post-hatching weather and nest predation. The data consists of 4,897 observations: 1,159 grouse cases  and 3,738 no-grouse cases.In this study, the winter data were used to gain information on the abundance of pine marten Data on human hunting were obtained also from LUKE. The hunting statistics have been collected with a harmonised method since 1996 and contain county-specific information on annual hunting bag by species. In most parts of our study area, willow grouse hunting was common in the early years of the study, while it has largely been non-existent since 2009. Yet, its inclusion was justified as this allowed to evaluate the effect of hunting in the decline.NorthBoreal and MidBoreal. Altogether, 2,487 triangles were counted from the MidBoreal climatic zone, on average 124 per year (standard deviation 22). From NorthBoreal, 1980 triangles were counted in total, on average 99 per year (standard deviation 19). Figure The study was conducted in areas where the willow grouse had been abundant enough since 1996 to assess any related patterns. Figure Snow data were gained from the Finnish Meteorological Institute (FMI), derived from snow depth measurement points located across Finland Fig. . Each da32. Now, each triangle (and for each year) gained the associated snow data from the snow depth measurement point that was closest to it. Next, monthly snow statistics were derived for each triangle . Here, it was known that the snow covers across the study area had diminished, and from earlier studies it was also hypothesized that the lack of snow during plumage changing will expose the willow grouse to increased raptor predation, which may drive their numbers down on a local scaleModelling between snow-related variables and willow grouse numbers was done using Generalized Linear Mixed Modeling (GLMM), applying the Poisson distribution with log link. The grouping of the data to different years and individual triangles was modelled by using random effects. As the clear decreasing trend in willow grouse numbers Fig.  could bei during year j was as follows:f is the nonlinear time trend, which was modelled by using restricted cubic splines using four knots placed at years 1999, 2003, 2007 and 2015, and the regression coefficients γ for the spline components. The spline retains the model as linear, where the predictors are 33.The final model included only one significant (p < 0.05) variable: the number of snow-free days in April. Therefore, the final model assessing the effect that snow-free April days have on adult willow grouse in triangle mentclass2pt{minimSF4ij−1 would be an artefact, which actually explains the effect of small-scale variability in the landscape on the grouse abundance instead of the effect of snow conditions of the previous winter. If that would be the case, then the two-years lagged variables SF4ij−2 should explain the variability in grouse abundance equally well as It might be possible that the effect of variable lmer, but also in the Bayesian framework using the Markov Chain Monte Carlo method as implemented in the R package MCMCglmm34. The default prior distributions of the package  were used. The trace plots showed good mixing of the MCMC chains. However, as both models led to similar conclusions with only marginal differences in parameter estimates, only the results based on the MCMC method are reported. Figures were drawn using the packages ggplot236 and cowplot37. In general, the GLMM approach was chosen as it allowed acknowledging the dependence caused by the grouping of the data to measurements within triangles35.To double-check the conclusions of the modelling, the model was fitted using traditional likelihood-based methods as implemented in the R-package The single most significant driver of willow grouse numbers (and the only significant one) was the amount of snow-free days in the preceding April . The other tested variables (Table SnowFreeDays_APR). From Fig. Results from the modelling showed that each additional snow-free day in April caused an additional 3.1% decline in willow grouse numbers  not directly to a warming climate, but to the fact that the warming climate caused declines in the arctic fox’s main prey, while aiding the range expansion of a stronger competitor, the red fox (Vulpes vulpes). In Canada, it has been suggested that conservation plans for the woodland caribou (Rangifer tarandus caribou) should account for the climate-induced range expansion of the moose 43.It is not straightforward, however, to state an observed pattern as a pure consequence of climate change or even the more frequent snow-free days, as a multitude of factors may be, and often are, involved. Indeed, cases where a species itself would not react to e.g. a warming climate, but is then influenced by competitors, predators or parasites that gain from the warming are anything but unheard of23. Despite the effects of hunting and mammalian predation being insignificant, the decline cannot be attributed to climatic changes alone. Indeed, field studies done in Sweden found raptors to be the most frequent cause of willow grouse mortality, also regardless of human hunting23. In Finland, the predation pressure by raptors has also been noted for other forest grouse species24, but in parts of our study area, the willow grouse was noted to be the most favoured prey among the different grouse species27. Furthermore, it is the only forest grouse changing into a white plumage, which in the event of a mismatch between plumage-changing and absence of snow would ruin its camouflage against a predator that is favouring it already. The recent Finnish Breeding Bird Atlas does not show a decline in the abundance of the birds of prey in the study region44.Here, the research setting and the long-term data allowed to include year- and area-specific variation and to exclude some of the potential alternative factors. Human hunting on willow grouse in our study area was minimal and in most parts, non-existent since 2009. The tested mammalian predators, red fox and pine marten are generally considered only as opportunistic predators; in a mortality study in Sweden, mammalian predators were responsible for zero willow grouse deaths during winter and spring46. Therefore, there should have been no other obvious reasons (than the mismatched winter plumage) for the populations decline due to snow-free springs. Here, we hypothesised that a white winter plumage in a snow-free landscape leads to increased predation pressure from birds of prey, and we were not the first ones to make the connection: in the 1930s, well before the drainage activities, the species declined sharply in southern and central Finland. The reasons behind this decline were linked to warmer seasons and prolonged snow-free periods, which were deemed to be potentially unsuitable for the species altogether, but at least exposing it to excess goshawk predation26. These southern parts of Finland were then later heavily affected by the drainage activities. In assessing willow grouse populations in Ostrobothnia region between 1965 and 1988 (southern extent of our study area), Tornberg and Sulkava27 discussed that snow-free seasons, springs in particular, caused a plumage mismatch “making the willow grouse exceptionally vulnerable to goshawk predation”.The periods when the effect of snow-free ground was assessed were the months when snow most typically arrives in (October and November) and disappears (April and May) from the study area. In addition, these are the months when the changing into and out of the winter plumage takes place. Snow-free landscape in autumn or spring is not only harmful for the willow grouse, as in such cases, the species would be able to use the most preferred source of food (berry plants) for a more prolonged period– Fig. 4). According to the parameter estimates, each snow-free day in April caused a decline of 3.1%  in the population. This alone does not sound dramatic, but as one observes the effect across the range of snow-free days in April  are most likely modelled by the time trend component of our model.The use of two-year lagged variable (number of snow-free days in April two year before) could not explain the variability in species abundance, when it was used instead of the one-year lagged predictor. This supports our conclusion that the decrease is associated with the mortality in the snow-free period of the previous April, instead of some local properties that are associated with the local average of the snow-free days: if the phenomenon was driven by variables of landscape structure, the effect would not have varied between two consecutive years – the land does not change its properties that fast, weather does. We also fitted a model where both the one-and two-year lagged snow-free days in April were included in the same model as predictors, but only the one-year lagged predictor was significant. Of course, the snow-cover induced local decrease in the abundance might be visible in the data also after two years. However, the local differences caused by local snow conditions of a given year will gradually disappear because the birds can move, and the 27, was made possible by long-term monitoring data on wildlife populations as well as on variables of weather. The value of these kinds of datasets is extremely high if we are to properly assess the impacts that the occurred climatic changes have had on our wildlife populations. Indeed, if one would have observed merely the average 20-year trend in the willow grouse numbers, the association of the decline to any given variable would have been possible, but any statements about the causal effect would have been very questionable. Our data allowed an analysis of the local annual anomalies from the overall trend in the abundance of the species, and explaining the deviations by local weather and snow cover conditions from the two preceding winters. Previous studies were used to construct hypotheses about the effects of snow cover, mammal predation and hunting pressure on the abundance. These hypotheses about the effect of snow-free ground were supported by our data, whereas the effects of mammal predation and hunting were so weak that they did not become statistically significant. Of course, it is always possible that the observed effect in an observational data set is caused by confounding factors instead of the true causal relationship. We protected ourselves against such misinterpretation by (1) restricting the analysis to only few carefully chosen potential predictors that are supported by the previous studies, (2) adjusting the results for the multiple tests, and (3) exploring whether the snow conditions of the previous spring could be replaced by snow conditions two years before the measurements. We conclude that, most likely, there is a causal relationship between the April snow conditions and willow grouse abundance of the following summer, and the relationship is caused by increased exposure of the white birds in the snow-free environment to their most significant predators (the birds of prey). After all, the white winter plumage is primarily meant to camouflage arctic species against predation19. Of course, a controlled experiment would be a better tool to analyse the causal relationship, but organizing such for the current research question would be practically impossible and unethical. Therefore, the current results shows, in our opinion, the strongest evidence from the best available data sets on the effect of diminishing snow covers on the abundance of willow grouse – a phenomenon discussed and assessed also in the past. The hypothesis is supported also by research done in North America and Italian Alps on other seasonally colour coating species such as the snow-show hare (Lepus americanus)50 or a close relative of the willow grouse, the willow ptarmigan (Lagopus muta)51.This study, as its predecessors52. Given that we know now the devastating role of drainage, conservation has still a good chance for success, given the species’ high reproductive output. Further research should thus be made on the additional drivers behind the population decline as these can turn out to be variables that, unlike weather, could be controlled by human actions. In Finland, severe conservation measures were started in the late 1990s, with the aim to restore peatland areas in central and southern Finland. These involved the filling of the ditches at some of the drained peatlands, for instance, which would eventually be beneficial also for the willow grouse and thus aid the return of the species. Field studies have confirmed that restored peatlands have been accepted as habitats by the willow grouse53. Yet, an equally topical question is also the ability of the species to track and adapt to the changed, and changing, snow conditions under the current climatic scenarios for boreal winters21. Indeed, while the species can decline even without a climatic effect52, a phenomenon such as warming or the prolonged snow-free periods has never been linked to an increase in willow grouse populations, but evidence from its declining effect is existing – as shown in this paper, in addition to the past papers. The current climatic predictions point to significantly diminishing snow covers in southern and central Finland54 – a change that is evident from past data as well. It seems that in the worst cases, the strongly light-controlled trigger that controls the camouflage of the willow grouse and other seasonally coat coloured arctic species19 is not in synchrony with what the species is trying to camouflage in, and these kinds of conditions are to become more frequent51.Past studies have shown that the willow grouse can revive given the right circumstances. After the decline of the 1930s, the late 1940s saw the willow grouse becoming abundant in parts of southern Finland again (though not as abundant as it was prior to the decline)