^{1}

^{1}

^{1}

^{1}

Considering the complexity and the criticality of the stacker equipment, in order to solve the problem that the stop accuracy of the stacker reduces or even fails to work due to abrasion of the running rail, this paper proposes a cooperative detection method based on Pulse Coupling Neural Network (PCNN) and wavelet transform theory to detect the abnormal points of the stacker running rail in industrial environment by analyzing the variation signals. First of all, considering the fact that the data is mixed up with noises because of the environment at the site and the possibility of the data acquisition equipment breaking down, a noise reduction method for the vibration signal data of stacker is constructed based on PCNN. Then, the basic theory of wavelet transform is introduced and then the rules of judging anomaly points on stackers’ running tracks are discussed based on wavelet transform. In addition, a cooperative detection method based on PCNN and wavelet transform theory is carried out based on the space-time distribution feature of the vibration of the stacker orbits in the industrial environment. Then the rationality of the proposed algorithm is verified by simulation through data provided by State Grid Measuring Center of China. This paper constructs a model of the abnormal point detection of the stackers in an industrial environment. The experimental simulation and example simulation show that the cooperative detection method based on PCNN and wavelet transform theory can effectively detect and locate the anomaly points of the stacker running tracks. The expansibility in engineering applications is promising. Lastly, some conclusions are discussed.

As is known to all, the stacker is a key equipment of automated storage and retrieval system (ASRS) in industrial environment. In practice scene of ASRS, the main function of the stacker is to grab, move, and stack goods from one shelf to another. Thus, the stability of stacker running track will influence the accuracy of grabbing and moving goods in practical engineering. As one of the key components of the stacker equipment, the track of the stacker is divided into upper and lower track. In fact, the stacking machine would wear, crack, sag, and bulge by long time running. And these defects will reduce the accuracy of the stacking machine. If the field engineer cannot detect and repair the defect as soon as possible, they may even cause the whole equipment to be worn and shut down. So, how to detect the anomaly point of stacker running rail is very important for safety performance of the whole system.

In anomaly detection, domestic and foreign researchers have made a lot of progress in all aspects. Since the 1980s, the anomaly detection problem has been widely researched in the field of statistics. For examples, [

Furthermore, Zhou S and Xu W have constructed the local anomaly detection algorithm based on the deviation in [

In addition, some scholars had discussed the anomaly detection in the frequency domain. For instance, to overcome the disadvantages that the window size does not change with frequency, the wavelet transform theory is usually introduced to compensate for the localization defects of the short-time Fourier transform [

Although the engineers and scholars have made a lot of achievements in the field of the detection of anomaly spot, the identifying and detection of abnormal data is still in its infancy of research for the stacker of ASRS. The practice application results show that there are still some problems in the methods of safety supervisory of the stacker of ASRS. As is known to all, the running performance of stacker is affected by various factors such as running environment, structural characteristics, and the optimal goal of the whole system. Hence, how to implement the detection of the abnormal points is the kernel problem of safety maintenance of stacker in ASRS. At present, there are some research achievements about the detection of a stacker’s running performance. But the research is mainly focused on the structure analysis or the design of the system, and few people have done their researches from the perspective of abnormal point’s detection [

However, because the running state of stacker is influenced by the state of the stacker’s component, the scene environment, the data acquisition equipment, and so on, the data set acquired from the system will contain a lot of noise. Obviously, the noise of data will reduce the accuracy of abnormal point’s judgment. Therefore, deleting and cleaning the noise from testing data is necessary to implement and accomplish the monitoring of running state of whole stacker system. To restrain the interferences of strong background noise, Huang D.R. and his coauthors have constructed a cooperated denoising algorithm for rolling bearing of stacker in [

Based on the analysis and the thesis above, to ensure the effectiveness of the incomplete data processing of real system, it is necessary to construct and design a cooperative anomaly detection algorithm so that the abnormal spot can be detected and located as quickly as possible in on-site industrial environment. Notice that the timing of the real time data process is vital in the industrial environment, and then the data signal needs to be treated from coarse to fine as soon as possible. On the basis, the Pulse Coupling Neural Network (PCNN) presented in [

Hence, the rest of this paper will discuss the details of the algorithm and thesis. The layout of the rest of the paper is organized as follows: Section

In a real working condition, the actual vibration signals measured from this system will be unavoidably affected by many complicated environmental factors. Obviously, the data package usually includes strong noises. So, to guarantee the effectiveness of anomaly detection for stacker running track, a reasonable data preprocessing procedure is very crucial to eliminate the noises that are contained in the dataset. In this context, constructing an effective denoising model and algorithm to process the original signal is of great theoretical and practical significance for the condition monitoring of the stacker running track.

However, most industrial monitoring and control applications require high performance, timeliness, and reliability. Then, most administrators and engineers hope to effectively operate the system without knowing the accurate model. Based on this thesis, the PCNN will be introduced later. On this basis, an improved PCNN denoising model and algorithm are analyzed and designed according to the actual situation to ensure the timeliness and stability of the performance of the stacker running track.

As we all know, PCNN is presented by Eckhorn based on the observed synchronous pulse transmission after the experiments of the cerebral cortex of the animals [

According to [

From the perspective of simulation, the PCNN neuron consists of three parts: receiving domain, modulation domain, and pulse generation domain. In real application, PCNN has the advantage that the data processing does not depend on precise mathematics model. That is to say, in the pretreatment of denoising, once the network interface of PCNN receives the input signal, the receiving field transmits it through two channels,

According to the link coefficient of

Basic structure of PCNN model diagram.

Obviously, the original dataset may be used to identify the character of noises by training the PCNN network. Of course, the noise-polluted data may be cleaned through analyzing the PCNN firing matrix and then the noises may also be filtered from the original dataset. In general, the engineers may test the abnormal point in a long data sequence to better locate the defect of stacker running track.

Unfortunately, although the basic structure of PCNN can clean the real dataset mixed with noise, the complexity of this topological structure can cause various issues that negatively impacts the engineer’s operation play experience. In real scenario of ASRS, the difficulty in condition monitoring is to ensure the timeliness of locating the abnormal position of stacker running track. In particular, because the running process of stacker is complex and changeable, the original dataset signified the running state of the stacker including lots of noise. From an operational perspective, the traditional denoising method based on nominal model may hardly achieve the expected denoising performance. So, it is necessary to simplify network structure to meet the actual demand and it is a nontrivial problem to construct an improved denoising algorithm based on the existing PCNN model to meet the actual needs.

In the industrial scenario, due to very poor measurement environment, the quality of the measurement signals may be affected by all kinds of factors. Meanwhile, the influential factors are connected with each other in vibration signals of stacker running track and they also have indirect effects. How to solve the coupling relations within the limits of real time control is very important to denoise the original dataset. In fact, considering that the basic topological structure of PCNN has the excessive parameters and the implementation is more complicated, it is not widely used in practice compared to the modified PCNN model. For a handy operation or statistics, the modified uncoupled model proposed in [

According to [

where

In this model, the signal from the channel

The modified topological structure of simplified PCNN is shown as Figure

Modified PCNN model diagram.

Obviously, the modified model has advantages of less parameters and simple implementation. In other words, the simplified denoising system has operational simplicity and high efficiency for the denoising processing of the raw incoming data. For the sake of applying in industry, the simplified denoising process is more applicable. Thus, we can make use of the modified denoising model to denoise the vibration signals of stacker running track and finally realize the recognition of anomaly points.

In the above section, one valid dimensional data cleaning model and framework was discussed and analyzed. Once the original dataset measured from the track running system was processed by the modified PCNN, the errors, noises, or missing data that are contained in the dataset should be eliminated and removed. That is to say, the output dataset may be used to accurately locate the anomalous point for the stacker running track of ASRS. Obviously, the key stage of locating the abnormal defect of stacker running track is to find a reasonable model. The engineering practice shows that the energy of induction signal induced by the abnormal point of the stacker running track concentrates on the high frequency band. Of course, the fact has also provided a basis for determining anomaly point of stacker running stacker. Based on this, it is imperative to find a reasonable way to decompose the output dataset of modified PCNN into two parts: low frequency part and high frequency part.

Simultaneously, because the wavelet transform developing since 80’s of last century has specific property of time-frequency localization, the method is especially fit for analyzing and detecting local signal mutation for the stacker running track of ASRS. Next step, the cooperative anomaly detection model of stacker running track will be constructed and analyzed based on wavelet transform.

In our experiments, the main feature of signal mutation is that the signal has local changes in time and space. To guarantee the accuracy of locating and identifying the defects of stacker running track, we have tried to design and construct a cooperative detection method combined with wavelet theory. The principle of using wavelet transform to detect the anomalous points is to decompose the signals in different resolutions. When the signal is abrupt, the coefficient gotten by the wavelet transform has a modulus maximum value. Therefore, the location of the outliers can be filtered out through the detection of the maximum modulus point.

Without loss of generality, the basic principle of wavelet transform is clearly defined: Suppose

where

In fact, when the output dataset of modified PCNN was decomposed into high frequency and low frequency, the key factor is to carry the expansion or contraction, and the translation based on the base wavelet. If the expansion or contraction factor is supposed as

where

So, for an arbitrary signal

Notice that the actual measured signals indicating the changes of the running state of the stacker running track are discrete in the stacker running track in ASRS, and the wavelet transform should be rewritten in a discrete form to treat the output dataset provided by modified PCNN. In general, the scaling factor

Then, the output dataset denoising by modified PCNN may be decomposed into high frequency and low frequency by the following formula.

In our experiments, if the raw output signal

The wavelet decomposing process of output dataset.

Obviously, according to the decomposing process in Figure

In practical project, the low-frequency coefficients reflect the contour of the original signal and the high-frequency coefficients describe the details of the signal. In particular, the singularity in the signals is often caused by a sudden change in frequency domain. For the engineers in health monitoring of stacker running state, it means that the high-frequency coefficients of wavelet transform can highlight singularity and can be used for detection and localization of the defect of the stacker running track. From the angle of engineering application, the damage of stacker running track will cause perturbations of measured signal at damage sites. Moreover, the measurement dataset is an aggregate of the running information, and the singularity of high frequency may depict the character of damage position on stacker running track. In other words, the damage concussion will cause the signal saltation. So, in practical engineering applications, it is very important to design a reasonable judgment rule of anomaly points.

To better locate the defects of stacker running track, the Lipschitz index is used to describe and design the judgment rule of singularity of the dataset. For the simplicity of analysis, the corresponding concept of Lipschitz index was defined as follows.

If there exists a constant

In general, the size of Lipschitz index is related to the value of the singularity in actual project; i.e., the more severe the degree of mutation, the steeper the peak of the catastrophic point, and the smaller the singularity index, and vice versa. Based on this thesis, we can define the local singularity of high frequency signals decomposed by wavelet transform as follows.

Notice that wavelet transform is applied to vibration signal analysis of stacker running track to detect the meshing abnormality of track with local defects, and the amplitudes of the vibration single will decrease or increase to some extent. So, by Definition

Notice that the mutation information of flaws may be accumulated in running process of stacker’s track, and the ability of a single high-frequency detail signal to reflect an abnormal point has limitations to locate the defect to stacker running track. To solve and overcome the problem, the product of the high-frequency coefficient, which can amplify the detail signal, is selected as the basis for the final judgment of the abnormal point in our experiments. To satisfy the need of engineering design, the accumulated information of track’s flaws can be described by using the following formula.

Then, the basic rule is shown as follows.

If a mutation appears in the product of the high-frequency coefficient, it is an abnormal point.

Through the analysis and rules above, once the output dataset processed by modified PCNN has been decomposed into the low frequency and high frequency components of the signals, the high frequency components can be used to detect and locate the anomaly points of stacker running track.

Based on the above analysis and discussion, combining with the modified PCNN and wavelet transform, the cooperative anomaly detection algorithm of the stacker running track may be designed in detail as below.

Normalize the data. Calculate the initial mean square error and initialize the network parameters by (

Use the normalized data as input data. End the loop if matrix

The noise points are determined according to the elements in the matrix, and then filter each data point.

Calculate mean square error (MSE), and compare it with the mean square error before, if the mean square error is smaller than the mean square error before, back to Step

Select wavelet base function and determine the number of layers of wavelet decomposition.

The wavelet transform coefficients of each layer are obtained by wavelet decomposition.

Multiply the detail signal to amplify the mutation signal.

Obtain the location of the outliers according to the location of the signal mutation.

The algorithm flow chart is shown as Figure

Flow chart of the algorithm.

To verify the noise reduction effect of modified PCNN, the simulation examples were first used to test the denoising ability of PCNN. In our simulation experiments, the sinusoidal signal was selected and adopted as the input data to train and test PCNN rule and the Gaussian white noise with a mean of zero and a variance of 1 is added to the sinusoidal signal as the experimental signal. The testing signal

where

In actual imitative preparation,

PCNN noise reduction results.

Simultaneously, to explain the validity of PCNN denoising algorithm, the wavelet threshold denoising algorithm was used to compare with the presented algorithm in our simulation examples. The effect of wavelet threshold denoising algorithm is shown as Figure

Wavelet threshold denoising results.

Obviously, although the comparison results between Figures

where

By (

Comparison of wavelet threshold denoising and PCNN noise reduction.

Wavelet denoising | PCNN denoising | |
---|---|---|

SNR | 15.15 | 16.47 |

MSE | 0.37 | 0.36 |

It can be seen in Table

In order to further verify the validity of cooperative anomaly detection method for singular point in signal dataset, a set of vibration signal with abnormal points is selected to test the effect of presented cooperative anomaly detection algorithm; i.e.,

In our simulation experiments, the simulation results are shown as Figure

Simulation result of cooperative anomaly extraction.

The original signal containing the exception point

Wavelet decomposition result

Abnormal point detection results

In fact, it can be seen from the simulation results that the sudden change of the signal appears at t=400 which can be observed from detail coefficients clearly. That indicates that the anomalies appear at t=400. It can be concluded that the presented cooperative anomaly detection can mark the location of the abnormal point of the vibration signal clearly. On the other hand, after testing the function, the presented cooperative algorithm may be applied to actual project.

Moreover, to further verify the validity of the proposed algorithm, the actual stacking machine vibration signal of ASRS, which has been developed and applied in State Grid Measuring Center of China, was selected to simulate the performance of the anomaly detection algorithm. The prototype systems of the stackers of State Grid Measuring Center of China is shown in Figure

Stackers in State Grid Measuring Center of China.

As can be seen in Figure

Basic structure of stacker running track.

Figures

In real application, the sampling time is from March to April of 2018. The size of the sampling data source measured from stacker running track is 7370. The data may contain noise because of the interference of the site environment and collecting data equipment and other reasons. To the Management Department of State Grid Measuring Center of China, the engineers especially want to find the anomaly points and locate the defects of stacker running track from the experimental data. If the engineers can do this, the whole security of ASRS may be better ensured. So, the simulation results between the original signal and compounded signal with noise caused by the defects of stacker’s running track were simulated in ASRS. In order to verify the effectiveness of the proposed model, wavelet transform and box-plot are chosen to compare with the result of PCNN-wavelet model. The results were shown as Figure

Comparison of abnormal point detection of three methods.

Data anomaly detection results based on wavelet

Data anomaly detection results based on box-plot

Results of data anomaly detection based on PCNN-wavelet

As seen from Figure

Comparison of abnormal point detection results.

Wavelet | Box-plot | PCNN-wavelet |
---|---|---|

| 1m-3.6m | 1.5m-2.0m |

| 5.4m-6.4m | 6.7m-7.6m |

| 11.8m-13.2m | 10m |

| 14.8m-16.1m | 17.8m |

| | 20m |

| 22.3m-23.2m | 22.4m |

Obviously, after the noise reduction of the input signal, the location of the abrupt change in the vibration signal may be depicted and described accurately by PCNN-wavelet. To ensure the operability in real engineering practice, some actual damage scenes of stacker running track were used to verify the effect of the presented algorithm. For instance, the actual testing and detecting sample photos at 1.5m, 7.2m, and 18 m are shown in Figure

Testing and detecting sample photos from scene.

Depression of lower track at 1.5m

Cracks appearing on upper track at 7.2m

Interface deformation on upper track at 18 m

In addition, there are rail welds at 10 m, 20 m, and 22 m, respectively.

From the experimental simulation results and the actual situation verification, although the box diagram can roughly locate the abnormal point interval, the PCNN-wavelet is more accurate and closer to the actual situation. In Figure

In fact, the emergence of data mutation points may be caused by the depressions, cracks, and deformation at the interface in the tracks. On the other hand, the response information of the damage position may be developed to make different damage positions in different information range. And the administrators of the industrial system may locate damage positions according to numerical characteristics in the damage unit. Furtherly, the relevant departments may design the good maintenance strategies according to the monitoring curves. That means our algorithm may be applied to the real project.

In this paper, a cooperative anomaly detection method for the stacker running track in the industrial environment is presented, which is based on PCNN and wavelet transform. Firstly, the data denoising model is built based on PCNN. Then, the data is detected by wavelet transform. Finally, the rationality and validity of the proposed method are verified by example analysis and simulation. The main conclusions are as follows:

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China under Grants 61703063, 61663008, 61573076, and 61004118; the Scientific Research Foundation for the Returned Overseas Chinese Scholars under Grant 2015-49; the Program for Excellent Talents of Chongqing Higher School of China under Grant 2014-18; the petrochemical equipment fault diagnosis Key Laboratory in Guangdong Province Foundation of China under Grant GDUPKLAB201501; the Chongqing Natural Science Foundation of China under Grant CSTC2017jcyjA1665; Science and Technology Research Project of Chongqing Municipal Education Commission of China under Grants KJ1605002, KJ1705121, KJ1705139, and KJZD-K201800701; the Program of Chongqing Innovation and Entrepreneurship for Returned Overseas Scholars of China under Grant cx2018110.

_{2}/