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Reliability and safety are major issues in tower crane applications. A new adaptive neurofuzzy system is developed in this work for real-time health condition monitoring of tower cranes, especially for hoist gearboxes. Vibration signals are measured using a wireless smart sensor system. Fault detection is performed gear-by-gear in the gearbox. A new diagnostic classifier is proposed to integrate strengths of several signal processing techniques for fault detection. A hybrid machine learning method is proposed to facilitate implementation and improve training convergence. The effectiveness of the developed monitoring system is verified by experimental tests.

Tower cranes are used extensively at construction sites to lift and move materials. They often rise hundreds of feet into the air, and can reach out just as far. As illustrated in

Reliability and safety are the main issues for tower crane applications. Machinery failures in tower cranes could result in catastrophic damage to life and

properties [

This work will focus on the condition monitoring of hoist units in tower cranes. The hoist unit is located in the counter jib as shown in

Condition monitoring is an act of fault diagnosis by means of appropriate information carriers such as temperature, acoustic signal, or vibration [

Fault diagnosis is a process of classifying the vibration features into different categories corresponding to different equipment health conditions. Automatic fault diagnosis can be conducted by either model-based or data-driven techniques [

In summary, when a monitoring system is used in real-world applications, unreasonably missed alarms (i.e., the monitor cannot pick up existing faults) and false alarms (i.e., the monitor triggers alarms because of noise instead of real faults) will seriously mitigate its validity. In addition, machinery dynamics may also change suddenly, such as just after repair or regular maintenance. To tackle these aforementioned challenges, the objective of this work is to propose a new adaptive NF (i.e., ANF in short), system for real-time health condition monitoring of hoist gearbox in tower cranes. It is new in the following aspects: 1) A new adaptive NF classifier is proposed for more accurate fault diagnosis in gear systems in order to provide a more reliable real-time condition monitoring tool for tower cranes. 2) A new hybrid training technique is proposed to facilitate training operation and improve training convergence. The effectiveness of the developed classifier is verified by experimental tests.

The remainder of this paper is organized as follows: the proposed intelligent monitoring system is discussed in Section 2. The effectiveness of the proposed techniques is verified experimentally in Section 3.

The developed intelligent monitor consists of several modules as illustrated in

A classical data acquisition system consists of hardware such as sensors, amplifiers, antialiasing filters, and a DAQ board. It is not only expensive but also inconvenient for real-world applications [^{2} pk. A distance smart sensor is used to measure gear rotation. Signal conditioning functions (e.g., amplification, rectification, and antialiasing filters) are implemented in IC filter chips so as to reduce size and cost. The wireless communication is based on SWAP protocol with frequency of 915 Hz. A user interface is developed to enable modification of DAQ reconfigurable parameters such as sensor calibration, sampling frequency, filter specifications, monitoring time interval, etc.

A novel ANF diagnostic classifier is developed for gear system monitoring. To improve monitoring accuracy, fault diagnosis is performed gear by gear by the use of time synchronous average filtering [

ℜ j : If ( x 1 is A 1 j ) and ( x 2 is A 2 j )

and ⋯ and ( x L is A L j ) ⇒ ( y ⊂ C j with w j ) (1)

where A l j are linguistic MFs of x l , l = 1 , 2 , ⋯ , L , j = 1 , 2 , ⋯ , J ; J is the number of rules; w j is the weight factor (contribution) of the rule ℜ j to the diagnostic operation.

The number of rules is associated with the diagnostic reasoning operations of input variables. For example, if the classifier has three inputs { x 1 , x 2 , x 3 } (i.e., L = 3 ), then diagnostic classification will be performed by the following criteria:

Four rules are associated with healthy condition ( C 1 ) reasoning: If (all three indices are Small), or (two are Small and one is Medium), then (the object is Healthy).

Four rules are associated with damage condition ( C 3 ) formulation: If (all three indices are Large), or (two are Large and one is Medium), then (the object is Damaged).

Except for these two states, the object is possibly damaged ( C 2 ), and the classification of C 2 is performed by 9 rules. In all of these cases, different feature association (rule) corresponds to a different weight grade w_{j}.

η j = ∏ l = 1 L A l j ( x l ) (2)

where A l j ( • ) denote MF grades.

Defuzzification is performed in layer 4. If J 1 , J 2 and J 3 are the number of rules associated with the classes C 1 , C 2 and C 3 , respectively, the belonging grade to each class is:

S 1 = ∑ J 1 η j w j ∑ J 1 η j S 2 = ∑ J 2 η j w j ∑ J 2 η j S 3 = ∑ J 3 η j w j ∑ J 3 η j (3)

The diagnostic indicator will be

y = S 1 ∨ S 2 ∨ S 3 . (4)

In machinery health condition monitoring, if the diagnostic indicator y ≤ ε 1 , the object is considered healthy; ε 1 is a threshold ( ε 1 = 0.50 in this case). If ε 1 < y ≤ ε 2 , the monitored object is possibly damaged; ε 2 is another threshold ( ε 2 = 0.70 in this case). Otherwise, if y > ε 2 , the object is damaged. An appropriate alarm should be given to the user for the occurrence of the defect.

When the indicator y values are formulated, the corresponding historical indicator y' in the database will be used to verify the diagnostic results so as to improve diagnostic reliability. In operation, the objective is to minimize the match error, e = | y − y ′ | , between the current value of the diagnostic indicator y and its comparator value y'. If y and y' belong to different classes, for example C 1 (healthy) and C 2 (possibly damaged), there are three possible reasons: 1) the defect recognized by the ANF classifier is caused by noise instead of real component damage; 2) the historical comparator data sets are not accurate; and 3) the convergence of the ANF classifier deteriorates due to local minima. These problems can be solved by the training process. For the first reason, the error-making rules will be punished to reduce their weight factors w_{j} to the diagnostic classification. If the database is not accurate, it will be updated using more accurate data sets for future monitoring and training application. If the errors are caused by possible trapping of location minima, the rule boundary properties in the decision space will be modified by appropriate training operations.

Once the ANF classifier is set up, it should be properly trained to improve its performance. In this case, a hybrid training strategy is suggested to update system parameters. The linear parameters will be trained by the use of the classical least squires estimator (LSE).

Many algorithms have been proposed in literature for nonlinear parameter optimization, each having its merits and limitations. The Levenberg-Marquardt (L-M) algorithm possesses quadratic convergence close to a minimum [

The objective or error function with respect to adjustable parameters θ k at the current time instant k is defined as

E ( θ k ) = 1 2 ∑ k = 1 K [ y k ( θ k ) − y d ] 2 = 1 2 ∑ k = 1 K r k 2 ( θ k ) = r k T ( θ k ) r k ( θ k ) (5)

where y k ( θ k ) is the kth output, k = 1 , 2 , ⋯ , K ; y d is the desired output. r k ( θ k ) is the error vector that can be either linear or nonlinear.

To simplify expression, the variable θ k is dropped in the related terms in these manipulations. By taking the Tayler series expansion and neglecting higher order terms,

θ k + 1 ≈ θ k + λ k ( J k T J k + η k I ) − 1 J k T r k = θ k + λ k H k − 1 J k T r k = θ k + ( 1 − α k ) H k − 1 J k T r k (6)

where J k ∈ R Z × Z is the Jacobin matrix; Z is dimension of θ k (or the number of parameters to be trained); H k ∈ R Z × Z is the Hessian matrix; I ∈ R Z × Z is an identity matrix; λ k = 1 − α k ; α k is the forgetting factor; η k is the learning that can be adapted by a line search method.

The Hessian matrix can be expressed as

H k = α k H k − 1 + ( 1 − α k ) ( J k T J k + η k I ) . (7)

In implementation, instead of computing the Z × Z matrix η t I at each time step, η t is added to one of the diagonal elements of J k T J k at each time instant

H k = α k H k − 1 + ( 1 − α k ) ( J k T J k + Z η k Λ ) (8)

where Λ ∈ R Z × Z has only one nonzero element located at t { mod ( Z ) + 1 } diagonal position, or

Λ i i ∈ { 1 , if i = k { mod ( Z ) + 1 } , and k > Z 0 , otherwise (9)

Correspondingly, Equation (8) can be rewritten as

H k = α k H k − 1 + ( 1 − α k ) ( U V − 1 U T ) (10)

where U T = [ J k T 0 ⋯ 0 1 0 ⋯ 0 ] , and V − 1 = [ 1 0 0 Z η k ] .

The computation of H k − 1 in Equation (6) is very time consuming, and it not suitable for real-time applications. Here H k − 1 is computed by using following approach:

( A + B C D ) − 1 = A − 1 − A − 1 B ( C − 1 + D A − 1 B ) − 1 D A − 1 (11)

where A, B, C and D are matrices such that A and ( C − 1 + D A − 1 B ) are nonsingular matrices.

Based on Equation (11), Equation (6) can be rewritten as

θ k + 1 = θ k + ( 1 − α k ) H k − 1 J k T r k = θ k + ( 1 − α k ) × { ( α k H k − 1 ) − 1 − ( α k H k − 1 ) − 1 ( 1 − α k ) U × [ V + U T ( α k H k − 1 ) − 1 ( 1 − α k ) U ] − 1 U T ( α k H k − 1 ) − 1 } J k T r k (12)

Let A = α k H k − 1 , B = ( 1 − α k ) U , C = V − 1 , and D = U T . From Equation (12), the recursive L-M algorithm can then be represented by

θ k + 1 = θ k + Φ k J k r k (13)

where Φ k = 1 α k [ Φ k − 1 − Φ k − 1 U S − 1 U T Φ k − 1 ] ,

S = α k V + U T Φ k − 1 U . (14)

S is a matrix with dimension 2 × 2; its inverse computation is simple and can be implemented for real-time monitoring applications. θ 0 = 0 ; Φ t is a covariance matrix with initial condition Φ 0 = ρ I , where ρ ∈ [ 10 2 , 10 6 ] , η k ∈ [ 0.001 , 10 ] , and α k ∈ [ 0.95 , 1 ] .

In hybrid training, as each data sample is inputted to the ANF classifier, the linear consequent parameters w j are updated by using the LSE. The nonlinear classifier MF parameters are trained by the use of the recursive L-M method. On the other hand, adaptive training is preferred in real-time applications because: 1) it is necessary for time-varying systems; 2) it possesses randomness that may help to escape from a local minimum; and 3) it is useful when the number of training data is large.

The effectiveness of the proposed ANF classifier techniques will be verified in this section by the use of experimental tests.

The experimental setup used in this study is schematically shown in

Gear fault consists of localized damage and distributed defects (e.g., wear and pitting). This work focuses on localized gear fault diagnosis because a localized fault can not only generate transmission errors but also may cause sudden failures [

broken out, the following teeth will be damaged quickly due to extra impacts, which could induce severe accidents in tower crane applications.

One of the initiatives of this work is to perform fault diagnosis of the gearbox gear by gear. Because the measured vibration is an overall signal generated from various rotary sources, the first step is to differentiate the signal specific to each gear by using the time synchronous average filter [

Several techniques have been proposed in the literature for gear fault detection; however, each has its own advantages and limitations, and is efficient for specific applications only [

1) wavelet energy function, using the overall residual signal that is obtained by bandstop filtering out the gear mesh frequency f R N and its harmonics, where f R is the rotation frequency (in Hz) of the gear of interest and N is the number of teeth of the gear;

2) beta kurtosis, using the overall residual signal;

3) phase demodulation using the signal average. Details of these techniques can be found from [

To verify the effectiveness of the developed intelligent monitor and the related techniques, systematic tests have been conducted corresponding to different machinery conditions. Three gear cases are tested in this case, as illustrated in

To make a comparison, two other related diagnostic classifiers are considered:

1) Classifier-1: A general ANFIS classifier, but using the proposed hybrid training technique with the LSE and the recursive L-M for training. It is to compare the proposed ANF classification scheme.

2) Classifier-2: It has the same network architecture with the ANF classifier, but the training is using the LSE and the classical L-M algorithm. It is to compare training efficiency of the proposed hybrid training based on the recursive L-M algorithm.

A series of tests have been conducted corresponding to different gear conditions. Firstly, both gears are healthy. The tests are undertaken with different load levels and speed. 225 data sets are collected for system training (120 pairs) and testing (105 pairs). Then the driven gear with a simulated crack is installed and tested. 300 data sets are collected; 200 pairs are used for training and 100 pairs for testing. In scored gear testing, similarly, 300 sets of data are collected; 200 pairs are used for training and 100 pairs for testing. Test results are summarized in

It is seen the developed ANF classifier provides best performance in this test, which has recorded 3 missed alarms and 2 false alarms during the testing periods. The missed alarms are mainly induced when the motor rotates at a very low speed, and the resulting signature modulation due to a small tooth crack is very weak. The false alarms are caused by the dramatic speed and load variations in testing. ANF classifier performs better than Classifier 1 that generates 5 missed alarms and 7 false alarms. It can verify the better classification efficiency of the proposed ANF diagnostic classification scheme. The developed ANF classifier also outperforms Classifier-2 that has recorded 4 missed alarms and 4 false alarms during the testing periods. It can verify the effective convergence of the proposed the recursive L-M algorithm.

The purpose of the developed ANF classifier is for hoist gearbox condition monitoring and diagnostics.

Diagnostic Classifier | Healthy Gears | Cracked Gears | Chipped Gears | Overall Accuracy % | |||
---|---|---|---|---|---|---|---|

MA | FA | MA | FA | MA | FA | ||

Classifier-1 | 1 | 3 | 2 | 2 | 2 | 2 | 88.4 |

Classifier-2 | 0 | 2 | 3 | 1 | 1 | 1 | 94.2 |

ANF Classifier | 0 | 1 | 2 | 1 | 1 | 1 | 98.8 |

A new ANF monitoring system is developed in this work for health condition monitoring of tower cranes, especially for hoist gearboxes. Vibration signals are measured using wireless smart sensors. Fault detection is performed gear-by-gear. A new ANF diagnostic classifier is developed to integrate strengths of several signal processing techniques for more accurate fault diagnosis. A novel hybrid training method based on a recursive L-M technique is proposed to improve processing efficiency by reducing the matrix size, and enhance the training convergence. The effectiveness of the proposed diagnostic techniques has been verified by experimental tests corresponding to different gear and operating conditions. Test results have demonstrated that the developed ANF monitoring system can provide more reliable fault diagnostics of the gear systems. It has also been implemented for real tower crane hoist drive system monitoring applications.

This work was supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC), Bare Point Water Treatment Plant, and eMech Systems Inc.

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

Adik, A.K. and Wang, W. (2019) An Intelligent System for Real-Time Condition Monitoring of Tower Cranes. Intelligent Control and Automation, 10, 155-167. https://doi.org/10.4236/ica.2019.104011