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In order to more effectively eliminate the disturbance of vibration signal to ensure the security monitoring of stacker be more accurate in Industrial Internet of Things (IIoT), a cooperative denoising algorithm with interactive dynamic adjustment function was constructed and proposed. First, some basic theories such as EMD, EEMD, LMS, and VSLMS were introduced in detail according the characteristics of stacker in IIoT. Meanwhile, the advantages and disadvantages of varieties of algorithms have been analyzed. Secondly, based on the traditional VSLMS-EEMD, an improved VSLMS-EEMD was proposed. Thirdly, to guarantee the denoising effect of security monitoring in IIoT, a cooperative denosing model and framework named as IDVSLMS-EEMD was designed and constructed based on the advantages of LMS, VSLMS, and improved VSLMS-EEMD. In addition, the assignment rules and models of the corresponding weight coefficients were also set up according to the features of the error signal of denoising process in IIoT. At the same time, we have designed a cooperative denoising algorithm with interactive dynamic adjustment function. And some evaluated indexes such as NSR and SDR were selected and introduced to evaluate the effectiveness of the different algorithms. Thirdly, some simulation examples and real experiment examples of stacker running signals under abnormal condition, which has been developed and applied in Power Grid of China, was used to verify and simulate the effectiveness of our presented algorithm. The experiment comparison results have shown that our algorithm can improve the denosing effect. Finally, some conclusions were discussed and the directions for future engineering application were also pointed out.

With the development and evolution of society, the Industrial Internet of Things (IIoT) plays a significant role in guiding the process of intelligent manufacturing for global industry [

At present, how to effectively eliminate and filter the disturbance noise from measured signals is the prerequisite for health monitoring of industrial systems [

To overcome the shortage, the multipoint mean smoothing denosing method was constructed and simulated to distinguish and separate useful signals from noise by the frequency difference in [

Furthermore, the wavelet theory was introduced to depict the characteristics according to the different amplitude of signals and noise in [

Based on this, many scholars and engineers have tried to construct and establish the improved model combined with EMMD and other methods such as LMS, Gath-Geva clustering, and so on in [

Based on this thesis, a cooperative denoising algorithm and model with interactive dynamic adjustment function have been analyzed and discussed in further section. The layout of this paper is arranged as follows. In Section

In practical engineering of IIoT, as we all know, the measurement signals are always typical and nonstationary, and they are the direct information resource of actual sense for IIoT, including running state, fault modes, and so on. Thus, the measurement signals obtained in actual IIoT contain inevitably strong background noise, which makes the useful information submerged. Obviously, the information features of health monitoring are not obvious for IIoT. Thus, how to design and find an effective denoising algorithm with interactive dynamic adjustment function is key step to guarantee the performance of safety maintenance of IIoT. Meanwhile, the denoising model and algorithm must achieve both timeliness and stability in health monitoring of IIoT. Only then can the work be of great theoretical and practical significance for nonstationary signals of health monitoring in IIoT.

On this basis, some basic theoretical models will be introduced and discussed for designing the cooperative denoising algorithm with interactive dynamic adjustment function in the next section.

For simplicity of analysis in health monitoring of IIoT, the measurement signal

According to the basic thesis, the detailed decomposition process of measurement mixed signals is shown as follows.

Suppose that the symbol

Combined with

Let

In that case,

Meanwhile, the new signal may be separated from the original signal by the following formula:

The filtering process in

It is rewriting the original signal

If we use the EMD to decompose the nonstationary signal in practice, there is one thing we have noticed: the EMD method has serious end effect and mode mixing of different time-scale IMF. Of course, the lacks caused by EMD signal decomposition will affect the denoising effect of the original signal in IIoT. So, how to improve the efficiency of noise reduction is very important in practice engineering. Next, we will introduce in depth the basic principles and related situations to establish an improvement algorithm.

To overcome the influence of the end effect and mode mixing in health monitoring of IIoT, an improved denoising algorithm named as Ensemble Empirical Mode Decomposition (EEMD) has been proposed based on EMD for signal denoising. The decomposition steps of EEMD are shown as follows.

It is adding a Gaussian random white noise

It is decomposing the new original signal

It is repeating

It is computing the average value of the IMFs obtained by decomposing the corresponding renewal signal with different Gaussian white noise; i.e.,

So, the decomposition results

In fact, the highest advantage of EEMD is that IMFs decomposed by the algorithm are independent and can prevent IMFs from mode mixing. In that case, it is vital to adaptively decompose the measurement signal of IIoT. But, as we all know, the effect of signal processing is always greatly influenced by choice of the decomposition threshold when EEMD is used to denoise for the measurement signal in IIoT.

Therefore, to further guarantee the effect and accuracy of selecting the decomposition threshold in processing the mixed signal, many engineers and researchers have tried to focus on finding out some helper methods to modify the defect of EMMD. Based on this, the typical LMS algorithm will be introduced to solve the problem of the decomposition threshold in further section.

In the security monitoring of IIoT, it is necessary to find an adaptive algorithm to reduce or inhibit the correlative noise. So, to get the more ideal signal,

For the sake of simplicity, the equalized signal of the training iteration is supposed as follows:

For the convenience of calculation, the above formula may be simplified as follows:

Although the algorithm may reduce the error accumulation effect in fine processing of nonstationary signal and improve the denoising accuracy, the convergence is slow. From a practical situation, one reason might be that the fixed step size cannot keep the insistency between the fast convergence speed and steady residual error [

As is well known, the denoising accuracy of nonstationary signal in IIoT is usually affected by varieties of factors, such as the testing environment, test methods, and so on. Furthermore, the training signals acquired by using LMS algorithm may still contain the strong noise because of the fixed step size. So, the amplitude of characteristic information cannot be evidently separated from the noise information. In brief, the residual noise has brought great obstacles for the denoising performance of nonstationary signal in IIoT. To overcome the problem, in this section, the variable step factor is inducted to the denoising control to balance the insistency between the fast convergence speed and steady residual error. The core of the thesis is that the step size can be dynamically adjusted according to the error signal of each training.

In formula (

In practical health monitoring of IIoT, we find the abnormal phenomenon that the error signal has the cumulative effect with experimental time. Further, the phenomenon results in the serious overlapping interference of denoising signal. So, to overcome the shortage, the error values at the current time and the last time are inducted to the adjustment of the step size. In other words, the step size may be gotten by the following formula.

Thus, the weight coefficients may be rewritten as follows:

In conclusion, the improved LMS with variable step factor can not only decrease the noise sensitivity but also improve the convergence performance. This is because of the improvement mentioned above that the improved weight coefficients can filter the influence of the cumulative effect in the training. Therefore, we can make use of the improved algorithm to denoise the nonstationary health monitoring of IIoT.

Obviously, we can see from the above analysis that each method has advantages and disadvantages in denoising process of nonstationary signal. If we may establish an integrated strategy to exert the advantages of each method and minimize the influence to disadvantages, thus the denoising effect of nonstationary signal may be vastly improved in health monitoring of IIoT. Next, the work will be in detail depicted.

To guarantee the denoising performance of nonstationary signal in health monitoring of IIoT, we have tried to design some cell modules to realize the task of the integration and configurable controls. With this goal, we have designed the LMS denoising module, VSLMS denoising module and proposed the improved VSLMS-EEMD denoising module based on the traditional VSLMS-EEMD, respectively. The denoising module by using LMS or VSLMS is shown as Figure

Denoising module of LMS or VSLMS.

In addition, to overcome the shortage of the VSLMS-EEMD proposed in [

Improved VSLMS-EEMD denoising module.

In fact, all these cell modules can be used to denoise of nonstationary signal in IIoT, and then each module can be used as a single denoising processor. However, the operations staff of health monitoring always want to highlight the advantages of these cell modules as large as possible. In order to maximize the denoising performance at each point, on the basis of the improved VSLMS-EEMD algorithm, a cooperative denosing algorithm with interactive dynamic adjustment function named as IDVSLMS-EEMD has been designed and constructed by using the stackable technology as Figure

Integrated cooperative denoising framework of IDVSLMS-EEMD.

Obviously, the framework can allow both those cell denoising modules (i.e., conventional and complementary) to exist in a framework that embarrasses neither. From an application perspective, the IDVSLMS-EEMD algorithm is a standardization of a set of denoising patterns based on a common set of denosing algorithm. So, one of the features of the IDVSLMS-EEMD model is able to move applications from one processor environment to another. From viewpoint of practical operation, the outputs of three denoising algorithms embedded in the IDVSLMS-EEMD framework are different, the differences can make up for each other’s mutual limitations. Therefore, the engineers can achieve the most optimal elimination at every point of the vibration signal for IIoT.

For the sake of analysis, relevant definition and calculation of the proposed cooperative denoising model IDVSLMS-EEMD are set as follows.

Firstly, the

From this model, the hub of the cooperative denoising framework is to determine the weights of denoising output at different time. In fact, if the denoising module is more suitable for nonstationary some point of signal in IIoT, the weight is bigger. Otherwise, the weight is smaller. But, for error signals, the opposite is true. So, it can be inferred that the error signal is inversely related to the weight coefficient, and the weight coefficient can be obtained by the error signal.

Define the error signal set at

According to the errors, the dynamical assignment rule of the weights is shown as follows.

The larger the error of single denoising processor is, the smaller the weight is. That is, consider the following.

(1) If

(2) If

(3) If

Through the assignment rule, the weight of every denoising module may be determined on each point according to the effect of denoising in IIoT. Obviously, the output of the single denoising module is ensured when the weight coefficient is dynamically adjusted in time. Of course, the denoising performance of the integrated system may be improved because each other makes use of mutual advantage and make up own shortage.

In the actual operation of integrated cooperative denoising framework, the success of achieving the performance goals depends on how well we develop the denoising strategy in health monitoring of IIoT. So, it is necessary to establish some scientific, systematic evaluation indexes of the cooperative denoising algorithm as feedback [

To evaluate the effectiveness of presented model, we have constructed two indexes according to the actual situation of health monitoring in IIoT. These evaluating indexes and rules are set as follows.

(1) Absolute Value Error is

By formula (

The bigger the C is, the worse the denoising effect is and vice versa.

(2) Normalized Cross Correlation (NCC) is

Similarity, the corresponding evaluation rule is designed as follows.

The larger the value of NCC is, the better the denoising effect is and vice versa.

So, the effect of the cooperative denoising model with interactive dynamic adjustment function may be evaluated by the above evaluation indexes.

Based on the above discussion, combining with the cooperative denoising framework, the cooperative denoising algorithm for nonstationary signal in IIoT may be designed in detail as below.

It is initialization of system. Load the original signal of IIoT and determine the states of the algorithm switches to be off or on.

Calculate the number of the switches that are on. If the number is equal to 3,

Obtain three denoised signals by using LMS, VSLMS, and VSLMS-EEMD denoising algorithms, respectively. The denoising process is divided into training stage and equaling stage.

(1) Training stage: for LMS denoising algorithm, the optimal weight coefficient

(2) Equalizing stage: the optimum weight coefficient

Obtain the dynamic adjustments of weight coefficients

(1) Obtain the error signal

(2) Obtain weight coefficients

Interactively denoising the IIoT signal by using (

Repeat

Evaluate denoising algorithms by using Rules

The cooperative denoising flow chart is shown as Figure

The cooperative denoising flowchart with interactive dynamic adjustment function.

To verify the effectiveness and rationality of the presented algorithm, the simulation examples were first used to test the denoising ability to the network data packet of health monitoring in IIoT. In general, the simulation original signal

In our simulation experiments,

In our simulation examples,

Comparison result between the original signal and noised signal.

Comparison result of the entire data sets (1-2000)

Refined comparison result of the data sets (1-200)

Further, to prove the efficiency and superiority of the improved VSLMS-EEMD and the proposed IDVSLMS-EEMD algorithm, some comparative simulations were done, including LMS, VSLMS, and wavelet with soft threshold combined with EEMD (WTS-EEMD) denoising model in [

Denosing simulation results of simulation signal by varieties of denoising algorithms (1-2000).

LMS denoised results (1-2000)

LMS denoised results (1-200)

VSLMS denoised results (1-2000)

VSLMS denoised results (1-200)

WTS-EEMD denoised results (1-2000)

WTS-EEMD denoised results (1-200)

VSLMS-EEMD denoised results (1-2000)

VSLMS-EEMD denoised results (1-200)

IDVSLMS-EEMD denoised results (1-2000)

IDVSLMS-EEMD denoised results (1-200)

Where, Figures

To compare the effect of varieties of denoising algorithms, we have selected the Noise Suppression Ratio (NSR) and Signal Distortion Rate (SDR) to evaluate denoising effect, which are defined as follows:

Without loss of the generality, the following rule needs to be noticed.

The larger the NSR is, the smaller the SDR will be. Meanwhile, this also means that the elimination effect of noise is better.

Based on the rule, the comparison results are shown in Table

Denosing evaluations of LMS, VSLMS, WTS-EEMD, VSLMS-EEMD, and IDVSLMS-EEMD.

Method/parameter | NSR | SDR |
---|---|---|

LMS | 0.7011 | 0.6266 |

VSLMS | 0.8369 | 0.3419 |

WTS-EEMD | 0.8603 | 0.5896 |

VSLMS-EEMD | 0.8644 | 0.2842 |

IDVSLMS-EEMD | 0.8674 | 0.2779 |

Combining with Figures

In addition, to illustrate the influence of noise, the comparison result of SNR between noised signal and denoised signal is also shown in Table

SNR of the noised and denoised simulated signal.

Signal/parameter | SNR |
---|---|

Noised signal | -1.1238 |

Denoised signal | 10.1160 |

As seen in Table

Denosing is the essential premise for further security analysis of stacker in IIoT. To further verify the performance of the proposed algorithm, the real-time simulation signal of stacker under abnormal condition in ASRS, which has been developed and applied in Power Grid of China, was selected to test the denoising performance of the presented algorithm. The test rig of the prototype systems in IIoT is shown as Figure

Simulate rigs of ASRS.

The simulation rig of ASRS is constructed and developed according to the real requirements of Power Grid in China. Their main function is to grab, move, and stack goods from one piece of equipment to another. As the crucial equipment of ASRS, the security and the positioning accuracy of stacker will directly affect the data acquisition and the data exchange of the whole IIoT system. In addition, the stacker is driven by motor, so the running state of stacker is directly reflected by the driving vibration signal. In real engineering, the test rig of stacker signal is shown as Figure

Test rig of stacker’ signal.

Driven motor

Depression of lower track

In real application, the sampling time is from a.m. 9:03:51 to p.m. 15:04. The column of starting and stopping range is from 0 to 23. The size of the detecting signal is 2000. Then, the comparison results between the original signal and compounded signal with noise measured were simulated by the stacker’s running. The results were shown as Figure

Comparison result between the original signal and noised signal of the stacker running.

Secondly, to further prove the efficiency and superiority of the improved VSLMS-EEMD and the proposed IDVSLMS-EEMD algorithm, some comparative experiments were done. The results of stacker’s running signal were simulated by the above relevant denoising algorithms, respectively. The denoising results were shown in Figure

Denosing simulation results of stacker’s running signal by using varieties of denoising algorithms (1-2000).

LMS denoised results of stacker’s signal

VSLMS denoised result of stacker’s signal

WST-EEMD denoised results of stacker’s signal

VSLMS-EEMD denoised results of stacker’s signal

IDVSLMS-EEMD denoised results of stacker’s running signal

To see more clearly the performance of denoising algorithm, we had selected the anterior 200 signals to refine the display degree of the denoising effect. The results are illustrated as Figure

Denosing refined simulation chart of stacker’s running signal by varieties of denoising algorithms (1-200).

LMS refined denoised effect of stacker’s signal

VSLMS refined denoised effect of stacker’s signal

WTS-EEMD refined denoised effect of stacker’s signal

VSLMS-EEMD refined denoised effect of stacker’s signal

IDVSLMS-EEMD refined denoised effect of stacker’s signal

Figures

Moreover, to quantitatively illustrate and assess the difference of denoising effect, we have used the evaluation indexes to compute the evaluated results. These values are listed in Tables

Simulation results of Rule

Signal/parameter | C |
---|---|

Original signal | 0 |

Noisy signal | 0.1424 |

LMS | 0.0823 |

VSLMS | 0.0820 |

WST-EEMD | 0.0810 |

VSLMS-EEMD | 0.0726 |

IDVSLMS-EEMD | 0.0589 |

Simulation results of Rule

Method/parameter | NCC |
---|---|

LMS | 0.7500 |

VSLMS | 0.7978 |

WST-EEMD | 0.8005 |

VSLMS-EEMD | 0.8429 |

IDVSLMS-EEMD | 0.8658 |

As measured in Table

The overall idea here is the same as what we have discussed in the previous simulation examples; the SNR between noised signal and denoised signal was also computed to illustrate the influence of noise for security analysis of stacker in IIoT. The numerical results are shown in Table

SNR of the noised and denoised signal for stacker.

Signal/parameter | SNR |
---|---|

Noised signal | -0.7437 |

Denoised signal | 14.6039 |

Obviously, the SNR is strengthened because the proposed algorithm may obtain and integrate more abundant information compared to traditional methods for security of stacker in real health monitoring of IIoT. That means that the effect of the cooperative denosing algorithm is very good.

The analysis results on the actual examples show that the proposed denoising algorithm may improve the accuracy of denosing to provide higher reliability for security monitoring of stacker in IIoT. That means that our algorithm may be applied to monitoring the security of the devices in the real IIoT.

In this paper the cooperative denoising algorithm with interactive dynamic adjustment function was depicted and analyzed based on LMS, VSLMS, and VSLMS–EEMD via the integrated optimization strategies. Meanwhile, some basic theories and corresponding evaluated indexes were also selected and established. The simulation examples and actual examples show the validity and rationality of the proposed algorithm in monitoring the security of real IIoT devices. The main conclusions of our work are listed as follows:

(1) In IIoT system, the original signal is seriously interfered by the surroundings resulting in low SNR. Because of this phenomenon, it is difficult to obtain accurate and reliable features from the confused signals, which has seriously hindered the security analysis, health detection, and the maintenance of IIoT system. Therefore, it is necessary to denoise the nonstationary signal of IIoT.

(2) The shortcomings of traditional EMD algorithm and traditional LMS algorithm with fixed step are considered. To maximize the advantages of LMS, VSLMS, and EEMD, the VSLMS-EEMD denoising algorithm has been constructed. On this basis, a cooperative denoising algorithm with interactive dynamic adjustment function is proposed to further improve the denoising accuracy of VSLMS-EEMD. Meanwhile, the evaluated indexes and rules were designed according to the features of the information for IIoT devices.

(3) Simulation examples and real data examples were used to implement and verify the efficiency of the proposed algorithm. Moreover, the comparison results were computed via the denoising evaluating indictors (i.e., model and rule). The simulation results show that the new algorithm has a better synchronous precision and security. Compared with the traditional method, the presented method can greatly reduce the noise ratio of security monitoring of IIoT devices.

Unfortunately, this cooperative denoising algorithm is only for one or three kinds of denoising algorithms, and no specific design is made for the cooperation of the two algorithms; the weight coefficients

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

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China under Grants 61573076, 61663008, 61703063, 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; 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, and KJ1705139 and KJZD-K201800701; the Program of Chongqing innovation and entrepreneurship for Returned Overseas Scholars of China under Grant cx2018110.