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Structural faults, such as unbalance, misalignment and looseness,

When building an intelligent system for condition diagnosis of plant machinery, symptom parameters (SPs) are required to express the information indicated by a signal measured for diagnosing machine faults. A good symptom parameter can correctly reflect states and condition trends of plant machinery [

Although many studies on intelligent condition diagnosis for plant machinery have been carried out using techniques such as neural networks (NN), support vector machines (SVM),

Ant colony optimization (ACO) is a new simulative evolutionary algorithm that is also called ant colony system (ACS) [

The faults (such as unbalance, misalignment or looseness,

For the above reasons, this paper proposes a novel method of intelligent condition diagnosis for rotating machinery developed by using relative ratio symptom parameters (RRSPs) and ant colony optimization (ACO). The RRSPs in the low-frequency domain are defined to reflect the features of vibration signals measured in each state. A synthetic detection index (

Many symptom parameters have been defined in the pattern recognition field, in this paper through analyzing the spectral features of structural faults of rotating machinery, the nine RRSPs in the low-frequency domain for structural faults diagnosis of rotating machinery are defined:
_{r}_{n}(f_{r})_{d}(f_{r})_{r}_{n}(if_{r})_{d}(if_{r})_{r}

Here, _{i}_{sn}_{hn}_{sd}_{hd}

Here, _{vn}_{vd}

Here, _{n}_{d}

Supposing that _{1} and _{2} are values of a symptom parameter (SP) calculated from the signals measured in state 1 and state 2, respectively, and conforming respectively to the normal distributions N(_{1},_{1}) and N(_{2},_{2}). Here, μ and σ are the average and the standard deviation of the SP. The larger the value of |_{2} − _{1}| is, the higher the sensitivity of distinguishing the two states by the SP. Because _{2} − _{1} also conforms to the normal distribution N(_{2} − _{1},_{1} + _{2}), there is the following density function about _{2} ≥ _{1} (the same conclusion can be drawn when _{1} _{2}). The probability can be calculated with the following formula:
_{0} is called the “Discrimination Rate (_{0} can be obtained by:

It is obvious that the larger the value of the _{0})” will be, and therefore, the better the SP will be. Thus, the

In order to effectively and automatically distinguish faults for condition monitoring of rotating machinery, a new intelligent condition diagnosis method is proposed based on the RRSPs and the ACO. The problem of state identification for the condition diagnosis is converted into the clustering problem of the RRSPs calculated by vibration signals measured in different states, which will be solved by the ACO.

The ACO algorithm introduced by Marco Dorigo in his Ph.D. thesis is a population-based meta-heuristic that can be used to find approximate solutions to difficult optimization problems. The ACO algorithm is inspired by the behavior of ants while finding paths from the colony to food. Ants have no sight and are capable of finding the shortest route between a food source and their nest by chemical materials called pheromones that they leave when moving. A moving ant lays some pheromone on the ground, thus making a trail of this substance. While an isolated ant moves practically at random, an ant encountering a previously laid trail can detect it and decide with high probability to follow it and reinforce the trail with its own pheromone. What emerges is a form of an autocatalytic process through which the greater the number of ants that follow a particular trail makes that trail more attractive to be followed. The process is thus characterized by a positive feedback loop, during which the probability of choosing a path increases with the number of ants that previously chose the same path [

ACO is a kind of heuristic algorithm with global optimization, which combines distributed computing and positive feedback mechanisms and has the following virtues:

Stronger robustness: ACO can transplant other problems, especially all kinds of assembled optimized problems.

Greater ability to find the better result: The algorithm adopts the positive feedback principle, which quickens the evolution processing and does not become trapped in local optima.

Distributing parallelism calculating: ACO is an evolution algorithm based on ant colonies and has parallelism base on them. The individual ants can continue to exchange and transfer the information (pheromone), which can lead to a better result.

It is easy to combine ACO with other methods: The algorithm can integrate other enlightened methods to improve the performance of the algorithm.

Assume that _{1},x_{2}_{n}_{1}∼P_{9}_{jk}

In this paper, the procedure for applying the ACO for the condition diagnosis is proposed as shown in

RRSPs used for reflecting the features of sample signals are inputted into the ACO.

Sample signals are randomly classified by artificial ants (artificial ants construct solutions), and the pheromone matrix is initialized.

According to the solutions, clustering centers are calculated by

Local search (refer to Section 4.4).

The pheromone matrix is updated (refer to Section 4.5).

According to pheromone matrix, artificial ants update the solutions (refer to Section 4.3).

Steps (3–6) are looped until the ending condition is satisfied.

In the ACO, every artificial ant will construct the solution _{i}_{i}_{i}_{i}_{i}_{i}_{ij}_{i}

Here, _{o}_{o}_{ij}_{i}

If _{o}_{i}_{ij}

To improve the efficiency and accelerate the convergence speed of the ACO, the method of local search for the ACO is presented. The local search method is conducted on all solutions or some solutions [

All solutions are arranged in ascending order according to the values of the objective function.

Random data _{i}

A weight

_{i}_{i}_{i}

The Euclidean distance between sample _{i}_{i}

Steps (2–6) are looped until the ten solutions are calculated.

Dorigo proposed three different models: the ant-cycle system, the ant-quantity system and the ant-density system [

Here, _{ij}_{i}_{ij(a)}

From _{i}_{ij}_{i}_{ij}

In this section, the application of condition diagnosis to a centrifugal fan is shown to verify that the method proposed in this paper is effective. To illustrate the effectiveness of the proposed method in the diagnosis of structural faults of rotating machinery, we also compare it with the conventional NN method.

The centrifugal fan for the diagnosis test and structural faults such as the normal (N), unbalance (UN), misalignment (M) and looseness (L) states is shown in

The RRSPs calculated by _{6}, _{7} and _{8}, and, when _{6}, _{7} and _{8} are singly used for distinguishing each state, the _{6}, _{7} and _{8} were larger than 95%. The combination of _{6}, _{7} and _{8} has high sensitivity for the structural faults diagnosis of the centrifugal fan. _{6}, _{7} and _{8}.

The main procedure for fault diagnosis using RRSPs and ACO was introduced in Section 1 (refer to _{6}, _{7}, _{8}) are selected for condition diagnosis by the _{6}, _{7}, _{8}, and the optimal clustering centers are obtained. Lastly, the condition of the centrifugal fan can be diagnosed by the trained ACO and RRSPs.

When a rotating machine is in a looseness state, the spectrum values in the high frequency region are obviously higher than in the misalignment and unbalance states. The symptom parameter _{6} indicates the ratio of the spectrum values between high frequency domain and low frequency domain. _{6} has high sensitivity for distinguishing the looseness state from other states. When a rotating machine is in a misalignment state, the vibration level in the shaft direction is stronger than in looseness and unbalance states. The symptom parameter _{7} is the ratio of the vibration level between the shaft direction and the horizontal direction, so _{7} has high sensitivity for distinguishing the misalignment state from other states. When a rotating machine is in an unbalance state, the vibration level of the vertical direction is stronger than in looseness and misalignment states. The symptom parameter _{8} is the ratio of the vibration level between the horizontal direction and the horizontal direction, so _{8} has high sensitivity for distinguishing the unbalance state from other states. Therefore, the combination of _{6}, _{7} and _{8} has high sensitivity for the structural faults diagnosis of the centrifugal fan.

In this research, the state identification for the condition diagnosis is converted to a clustering problem for the values of the RRSPs calculated from vibration signals measured in different states of the centrifugal fan. The ACO automatically finds the optimal clustering centers and classify all sample data according to the amount of information around the clustering centers. The purpose of training the ACO is the acquisition of optimum clustering centers. _{6}, _{7} and _{8} calculated using the vibration signals measured in each known state were input into the ACO. After about 150 iterations, the ACO converged to the optimum clustering centers.

Here, the symbols ⋄, ○, ☆ and Δ express the value samples of RRSPs in the normal state, unbalance state, misalignment state and looseness state, respectively, and the big symbols represent their clustering centers.

In the training process of the ACO, at first, the sample data are classified into normal, unbalance, misalignment and looseness states randomly. The clustering centers and the sum of the spatial distance between every sample data and the clustering centers are calculated by

Here, x is the coordinate value of clustering center on the _{6} axis, y is the coordinate value of clustering center on the _{7} axis, z is the coordinate value of clustering center on the _{8} axis. After training the ACO, to verify the diagnostic capability of the proposed method in this paper, the test data measured in each known state that had not been used to train the ACO were used. When inputting the test data into the trained ACO, the ACO classified the test data according to the information of the optimum clustering centers shown in

To summarize the condition diagnosis method proposed in this paper for a rotating machine,

In order to compare the performances of the ACO and a neural network (NN) for the condition diagnosis, a NN was also built, which consisted of the input layer, the hidden layer and the output layer, as shown in _{N}, D_{UN}, D_{M}, D_{L}, which indicate the normal (N), unbalance (UN), misalignment (M) and looseness (L) states, respectively. The flowchart of fault diagnosis by the NN is shown in

In this paper, when the NN was applied to fault diagnosis, the diagnostic knowledge (teaching data) for the NN was acquired by probability theory using the probability distributions of the RRSPs (_{6}, _{7}, _{8}) calculated by the vibration signals measured in each known state and selected by _{N}_{iN}_{iN}_{iN}_{iN}

For condition diagnosis using two or more RRSPs, the possibility grades _{N}

To train the NN, the training data obtained by the method mentioned above were input into the NN. After about 10,000 iterations, the NN converged. As an example, part of the acquired training data for the NN is shown in

After training the NN, the faults of the centrifugal fan were diagnosed with the learned NN. To compare the efficiency of the method proposed in this research with the NN, the same test data used in the ACO were input into the learned NN. As an example, some of the diagnosis results are shown in

According to the diagnosis results shown in

The reasons of the low diagnosis accuracy by using the NN are thought to be: (1) Conventional NN cannot reflect the possibility grades of the ambiguous diagnosis problems. (2) Conventional NN will never converge when the symptom parameters inputted in the 1st layer have the same values in different states.

In order to detect faults and distinguish fault types at an early stage, this paper proposes a new method for diagnosing structural faults of rotating machinery developed by using relative ratio symptom parameters (RRSPs) and ant colony optimization (ACO). The main conclusions can be summarized as follows:

The nine symptom parameters called “relative ratio symptom parameters” in the low-frequency domain were defined for reflecting the features of vibration signals measured in each state.

The state identification for the condition diagnosis of rotating machinery was converted to a clustering problem of the values of the relative ratio symptom parameters (RRSPs) in the low-frequency domain, calculated from vibration signals in different states of the machine. Ant colony optimization (ACO) was also introduced for this purpose.

The synthetic detection index (

A comparison was made between the proposed method and a neural network (NN), and the practical example of faults diagnosis of the centrifugal fan verified the effectiveness of the proposed method. The diagnosis results showed that the structural faults which occur in the centrifugal fan, such as unbalance, misalignment and looseness states,

In this paper, we have verified the efficiency of the ACO diagnosis system in order to detect faults and distinguish fault types at an early stage. For the future study, we will apply the method to detect and diagnose faults at every fault stages, such as initial stage fault, moderate stage fault and serious fault

Flowchart of the condition diagnosis.

Flowchart of ACO for condition diagnosis.

Experiment system for the fault diagnosis

Structural faults

Raw vibration signals in time domain

Raw vibration signals in frequency domain.

The change of the clustering centers while training the ACO for the condition diagnosis of the centrifugal fan.

Pheromones for distinguishing the normal state from abnormal states.

The flowchart of the condition diagnosis using the ACO system.

NN for pattern recognition in fault diagnosis.

Flowchart of fault diagnosis by the NN.

_{max} |
_{min} | ||
---|---|---|---|

P_{1}P_{2}P_{3} |
48.67 | 9.8 | 0.31 |

P_{1}P_{2}P_{4} |
27.26 | 5.67 | 0.41 |

… | … | … | … |

P_{6}P_{7}P_{8} |
94.60 | 9.66 | 1.75 |

P_{6}P_{7}P_{9} |
81.16 | 9.66 | 0.27 |

P_{6}P_{8}P_{9} |
69.04 | 7.83 | 0.27 |

P_{7}P_{8}P_{9} |
65.24 | 9.66 | 0.27 |

_{6}, _{7} and _{8}.

_{6} |
_{7} |
_{8} | |
---|---|---|---|

_{N-M} |
7.65 | 5.80 | 3.36 |

_{N-L} |
6.63 | 6.18 | 2.40 |

_{N-UN} |
5.42 | 2.71 | 5.74 |

_{M-L} |
7.83 | 1.75(_{min} |
1.85 |

_{M-UN} |
2.66 | 9.66(_{max} |
2.13 |

_{L-UN} |
7.57 | 8.87 | 6.37 |

Parameters of the ACO.

Weight value for updating solution _{o} |
0.5 |

Parameter of heuristic information |
0.6 |

Weight value of local search |
0.2 |

Decay parameter of pheromone |
0.1 |

Parts of acquired data of diagnosis for the ACO.

RRSPs | Clustering Center | ||||
---|---|---|---|---|---|

P_{6} |
P_{7} |
P_{8} |
x | y | z |

1.126 | 1.033 | 0.749 | 1.056 | 1.005 | 0.913 |

0.941 | 0.938 | 1.099 | |||

1.260 | 0.967 | 0.967 | |||

… | … | … |

RRSPs | Clustering Center | ||||
---|---|---|---|---|---|

P_{6} |
P_{7} |
P_{8} |
x | y | z |

0.430 | 0.772 | 0.181 | 0.501 | 0.827 | 0.223 |

0.525 | 0.779 | 0.244 | |||

0.588 | 0.851 | 0.181 | |||

… | … | … |

RRSPs | Clustering Center | ||||
---|---|---|---|---|---|

P_{6} |
P_{7} |
P_{8} |
x | y | z |

0.352 | 1.366 | 0.319 | 0.342 | 1.397 | 0.416 |

0.329 | 1.307 | 0.452 | |||

0.302 | 1.440 | 0.506 | |||

… | … | … |

RRSPs | Clustering Center | ||||
---|---|---|---|---|---|

P_{6} |
P_{7} |
P_{8} |
x | y | z |

5.748 | 1.461 | 0.595 | 5.256 | 1.533 | 0.581 |

4.799 | 1.636 | 0.534 | |||

4.963 | 1.481 | 0.540 | |||

… | … | … |

Diagnosis result using proposed method.

| |||||||
---|---|---|---|---|---|---|---|

_{6} |
_{7} |
_{8} |
|||||

| |||||||

1.084 | 0.937 | 0.854 | 0.296 | 0 | 0 | 0 | N |

0.976 | 1.114 | 0.901 | 0.296 | 0 | 0 | 0 | N |

0.430 | 0.772 | 0.181 | 0 | 0.296 | 0 | 0 | UN |

0.509 | 0.856 | 0.255 | 0 | 0.296 | 0 | 0 | UN |

0.345 | 1.445 | 0.277 | 0 | 0 | 0.296 | 0 | M |

0.388 | 1.399 | 0.563 | 0 | 0 | 0.296 | 0 | M |

5.049 | 1.589 | 0.527 | 0 | 0 | 0 | 0.296 | L |

5.530 | 1.514 | 0.618 | 0 | 0 | 0 | 0.296 | L |

… | … | … | … | … | … | … | … |

Training data for the NN.

| ||||||
---|---|---|---|---|---|---|

_{6} |
_{7} |
_{8} |
||||

| ||||||

0.871 | 0.913 | 0.662 | 1 | 0 | 0 | 0 |

1.051 | 1.014 | 0.884 | 1 | 0 | 0 | 0 |

1.231 | 1.115 | 1.106 | 1 | 0 | 0 | 0 |

0.290 | 1.311 | 0.241 | 0 | 1 | 0 | 0 |

0.337 | 1.398 | 0.412 | 0 | 1 | 0 | 0 |

0.384 | 1.485 | 0.583 | 0 | 1 | 0 | 0 |

3.994 | 1.403 | 0.498 | 0 | 0 | 1 | 0 |

5.247 | 1.541 | 0.593 | 0 | 0 | 1 | 0 |

6.500 | 1.679 | 0.688 | 0 | 0 | 1 | 0 |

0.385 | 0.768 | 0.145 | 0 | 0 | 0 | 1 |

4.488 | 0.843 | 0.215 | 0 | 0 | 0 | 1 |

0.591 | 0.918 | 0.285 | 0 | 0 | 0 | 1 |

… | … | … | … | … | … | … |

Diagnosis result using the NN.

| |||||||
---|---|---|---|---|---|---|---|

_{6} |
_{7} |
_{8} |
|||||

| |||||||

1.084 | 0.937 | 0.854 | 0.988 | 0 | 0.018 | 0.009 | N |

0.976 | 1.114 | 0.901 | 0.996 | 0 | 0.004 | 0.013 | N |

0.430 | 0.772 | 0.181 | 0.001 | 0.560 | 0 | 0.444 | × |

0.509 | 0.856 | 0.255 | 0.001 | 0.562 | 0 | 0.443 | × |

0.345 | 1.445 | 0.277 | 0.005 | 0 | 0.993 | 0.005 | M |

0.388 | 1.399 | 0.563 | 0.005 | 0 | 0.992 | 0.007 | M |

5.049 | 1.589 | 0.527 | 0.001 | 0.561 | 0 | 0.443 | × |

5.530 | 1.514 | 0.618 | 0.001 | 0.517 | 0 | 0.418 | × |

… | … | … | … | … | … | … | … |