Health-diagnosis of electromechanical system with a principal-component bayesian neural network algorithm

Abstract

This study proposes a cloud tele-measurement technique on an electromechanical system, and uses a neural network algorithm based on principal-component analysis (PCA) to quickly diagnose its performance. Three vibration, three temperature, electrical voltage, and current sensors were mounted on the electromechanical system, and the external braking device was used to provide different load-states to simulate the operating states of the motor under different conditions. Moreover, a single-chip multiprocessor was used through the sensor to instantly measure the various load-state simulations of the motor. The operating states of the electromechanical system were classified as normal, abnormal, and required-to-be-turned-off states using a principal-component Bayesian neural network algorithm (PBNNA), to enable their quick diagnosis. Furthermore, PBNNA successfully reduces the dimensionality of the multivariate dataset for rapid analysis of the electromechanical system’s performance. The accuracy rates of health-diagnosis based on the Bayesian neural network algorithm and PBNNA models were obtained as 97.7% and 98%, respectively. Finally, the single-chip multiprocessor based on PBNNA is used to automatically upload the measurement and analysis results of the electromechanical system to the cloud website server. The establishment of this model system can optimize prediction judgment and decision-making based on the damage situation to achieve the goals of intelligence and optimization of factory reconstruction.

Keywords

Tele-measurement electromechanical system principal-component bayesian neural network algorithm health-diagnosis cloud website server

1 Introduction

According to Industry 4.0 technology development, improving work efficiency and productivity in a safe environment is the focus of industrial technology development worldwide [1 –3]. Therefore, it is important to focus on the operating efficiency of production machines and how to avoid losses caused by unpredictable shutdowns due to machine damage. Through the health-diagnosis of the electromechanical system, early maintenance and replacement of parts can be performed. To achieve continuous safe operation, condition monitoring is widely used in the utilization of modern equipment to extend and prevent equipment damage. Failure of the electromechanical system may lead to loss of life for the operator, resulting in a need for reliable fault detection, diagnostic prompts, and accuracy. The most important aspect in a production factory is power equipment. Among them, the motor is an indispensable device. Most electromechanical system signals are complex and involve many variables. However, supervisory control and data acquisition (SCADA), commonly used in factories, only provides data-based warnings and cannot diagnose system states. Vibration signals have been widely used to monitor electromechanical systems using accelerometers [4 –6]. Some studies utilize power spectrum, wavelet decomposition, etc. to extract the features of the electromechanical system [7 –11]. In addition, the literature utilizes a support vector machine [12 –14] or neural network algorithm [15 –17] to analyze the performance of the electromechanical system. All the above methods require considerable data to perform calculations for the performance analysis, which will consume significant amount of time and technological resource. According to the literature [18 –22], principal component analysis (PCA) reduces the dimensionality of the multivariate dataset to quickly analyze the main characteristics of the dataset. To analyze the possibility of uncertain events for the influence relationship between variables, the Bayesian neural network algorithm (BNNA) based on a graphical statistical inference model [23 –25] is utilized. For quick diagnosis of the operating states of the electromechanical system, this study classifies them as normal, abnormal, and required-to-be-turned-off states by using a BNNA based on a PCA. BNNA and PCA are integrated to develop a principal-component Bayesian neural network algorithm (PBNNA). A single-chip multiprocessor is used to instantly measure the vibration, temperature, and electrical characteristics of the running electromechanical system, and automatically upload the measurement-analysis results to the cloud website server. Therefore, a remote diagnosis of the electromechanical system can be obtained through the cloud website information, thereby reducing the time-labor cost of obtaining information. The establishment of this model system can optimize prediction judgment and decision-making based on the damage situation to greatly improve the management efficiency, and achieve the goals of intelligence and optimization of factory reconstruction.

2 Tele-measurement structure of electromechanical system

In this study, the electromechanical system comprises a motor, an electric motor generator, and a braking device. The electric motor generator based on a compound DC machine with both shunt and series field windings, generates electrical power for a light bulb (220 V, 60 W) by the mechanical power output of the motor, as shown in Fig. 1. An external braking device is used to provide different load states to simulate the operating state of the electromechanical system under different conditions of power generation. To diagnose the operating states of the electromechanical system, three vibration, three temperature, electrical voltage, and current sensors are mounted on the electromechanical system, as shown in Fig. 2. A single-chip multiprocessor is used to immediately measure the vibration, temperature, and electrical characteristics of the running electromechanical system, and automatically upload the measurement and analysis results to the cloud website server.

Fig. 1

Photograph of (a) electric motor generator, (b) motor, and (c) circuit diagram of electric power generation.

Fig. 2

Tele-measurement structure on electromechanical system.

Figure 3 depicts a single-chip multiprocessor (Arduino Mega), an RS-485 Transceiver (MAX 485), an accelerator (ADXL345), a WiFi module (ESP8266), two programmable signal converters (BCT210), three thermometers (PT100), and a multimeter (TCS98D) for tele-measurement and analysis. The vibrations of X, Y, and Z axes of the electromechanical system are measured by an accelerator. The X, Y, and Z axes are in the direction of the rotation axis, perpendicular to the horizontal, and vertical directions of the rotation axes, respectively, as shown in Fig. 2. The thermometer 1, 2, and 3 measure the temperatures of the field winding, the shell of electric motor generator, and room temperature, respectively, as shown in Fig. 2. Fig. 4 represents the circuit diagram of tele-measurement and analysis.

Fig. 3

Photos of (a) single-chip multiprocessor (Arduino Mega), (b) RS-485 transceiver (MAX 485), (c) accelerator (ADXL345), (d) WiFi module (ESP8266), (e) programmable signal converter (BCT210), (f) thermometer(PT100), and (g) multimeter (TCS98D) for tele-measurement and analysis.

Fig. 4

Circuit diagram of tele-measurement and analysis.

3 Health-diagnosis method using PBNNA

For a quick diagnosis of the states of the electromechanical system, this study utilizes PBNNA to classify them as normal, abnormal, and required-to-be-turned-off states by three vibration, three temperature, electrical voltage, and current measurement parameters of the electromechanical system. According to the literature [21, 22], Pearson [21] first utilizes PCA to estimate the principal components of the multivariate dataset by a statistical formulation. In addition, PCA optimally reduces the dimensionality of the multivariate dataset that facilitates a quick analysis of the main characteristics. This study assumes that x is a set of measurement parameters x ∈ R^K, and integer k is less than K. The k “principal components” of x, y ∈ R^k, are defined as the k uncorrelated linear components of x [22]: $y_{i} = v_{i}^{T} x$ (1) where y_i ∈ R and v_i ∈ R^K for i = 1, 2, …, k. The necessary condition of the k principal components of x is $Var (y_{1}) ⩾ Var (y_{2}) ⩾ \dots ⩾ Var (y_{k}) > 0$ (2) where Var (y_k) is the variance of y_k. To find the k principal components y_i, $y_{i} = v_{i}^{T} x$ and $y_{j} = v_{j}^{T} x$ for i ≠ j are required to be uncorrelated. To solve this for v_i, this study uses the method of Lagrange multipliers [22]. The extremum of the Lagrangian function is obtained as $L = v_{i}^{T} Σ_{x} v_{i} + λ_{i} (1 - v_{i}^{T} v_{i}) + \sum_{j = 1}^{i - 1} ρ_{j} v_{i}^{T} v_{j}$ (3) where $Σ_{x} \dot{=} E [{xx}^{T}]$ is a covariance matrix of x and rank (Σ_x) ⩾ k. By computing the derivatives of L with respect to (v_i, λ_i) and setting them to zero, the necessary conditions for (v_i, λ_i) to be an extremum of L are obtained as $Σ_{x} v_{i} + \sum_{j = 1}^{i - 1} \frac{ρ_{j}}{2} v_{j} = λ_{i} v_{i}$ (4) where $v_{i}^{T} v_{i} = 1$ , $v_{i}^{T} v_{j} = 0$ , and j = 1, 2, …, i - 1. Equation (4) can be rewritten as $v_{j}^{T} Σ_{x} v_{i} + \frac{ρ_{j}}{2} = λ_{j} v_{j}^{T} v_{i} + \frac{ρ_{j}}{2} = λ_{i} v_{j}^{T} v_{i}$ (5)

Solving Equation (5) gives $ρ_{j} = 2 (λ_{i} - λ_{j}) v_{j}^{T} v_{i} = 0$ (6)

Since the associated extremum value is $v_{i}^{T} Σ_{x} v_{i} = λ_{i} = Var (y_{i})$ , v_i is the leading eigenvector of Σ_x based on the leading eigenvalue λ_i restricted to the orthogonal complement of the span of v₁, …, v_i-1. Since the eigenvalues of Σ_x are distinct, v_i is the eigenvector of Σ_x associated with the ith largest eigenvalue.

According to the literature [26 –28], neural network algorithms imitate the learning of human brains to realize actions based on different stimuli. The approximation and optimization functions of the actions can be expressed by the training of samples or data. To analyze the possibility of uncertain events for the influence relationship between variables, the BNNA based on a graphical statistical inference model [23 –25] is utilized. Therefore, the BNNA based on the k principal components of eight measurement parameters is utilized to quickly diagnose the motor operating states.

In the Bayesian network algorithm [23], the objective function of regularization is $F = α W_{ɛ} + β W_{δ}$ (7) where $W_{ɛ} = \sum_{i = 1}^{M} ɛ_{i}^{2}$ is the sum of squares of N network weights, and α and β are parameters of the objective function. $W_{δ} = \sum_{i = 1}^{k} {(t_{i} - a_{i})}^{2}$ . Here, k is the number of k principal component inputs of eight measurement parameters in the training set, t_i is the ith expected output, and a_i is the ith output obtained as the neural network response. If β ⪢ α, overfitted training occurs and overemphasizes the training data. Conversely, if α ⪢ β, overemphasized training occurs to reduce the weight size for tolerating higher errors. According to the literature [25] for determining the optimal values of α and β at ω^MP, the main result is obtained as ${\begin{matrix} α^{MP} = \frac{γ}{2 W_{ɛ} (ω^{MP})} \\ β^{MP} = \frac{k - γ}{2 W_{δ} (ω^{MP})} \end{matrix}$ (8) where γ = M - 2α^MPtr (G^MP) ^-1 is called the effective number of parameters, which is basically the degrees of freedom in the neural network, which in turn is the number of weights and biases effectively used by the network. G = α ∇ ²W_ɛ + β ∇ ²W_δ is the Hessian matrix of the objective function. ω^MP is the minimum point of the posterior density, where the gradient is zero. Eventually, this study utilizes the Levenberg–Marquardt algorithm [29] to minimize the objective function F of the regularization. The Hessian matrix of the objective function, by using the Gauss–Newton approximation is obtained as $G = \nabla^{2} F \approx 2 α μ I_{M} + 2 β J^{T} J$ (9) where μ is the scalar parameter for the approximate Hessian matrix and J is the Jacobian matrix of the training set errors [30]. Substituting Equation (9) into (8) computes the new α and β estimate parameters for the objective function. Consequently, the PBNNA model is completely set up to work until convergence of the objective function by iterative computation of Equations (8) and (9) is achieved.

4 Design of PBNNA

For the health-diagnosis of the electromechanical system, three vibration, three temperature, electrical voltage, and current sensors are mounted on the electromechanical system in Fig. 2. This study utilizes an external braking device to provide different load states to simulate the operating states of the electromechanical system under normal, abnormal, and required-to-be-turned-off conditions. Simultaneously, a single-chip multiprocessor is used to instantly measure the vibration, temperature, and electrical characteristics of the electromechanical system under the three operating states. Since the electromechanical system generates electrical power to drive a light bulb, this study utilizes the electrical power parameter of the light bulb to classify the electromechanical system states as normal, abnormal, and required-to-be-turned-off. When the power of the electromechanical system is greater than or equal to 1.8 W and less than 10 W, the system is in a normal state. When the power of the electromechanical system is greater than or equal to 0.8 W and less than 1.8 W, the condition of the system is in an abnormal state. Finally, when the electromechanical system generates less than 0.8 W, the condition of the system is required-to-be-turned-off. Table 1 depicts the conditions of normal, abnormal, and required-to-be-turned-off states.

Table 1
Conditions of normal, abnormal, and required-to-be-turned-off states

Item Electrical power (W) Light-bulb state

Normal ≥1.8 and <10 Full bright

Abnormal ≥0.8 and <1.8 Haft bright

Requirement to be turned off <0.8 Weak bright

Item	Electrical power (W)	Light-bulb state
Normal	≥1.8 and <10	Full bright
Abnormal	≥0.8 and <1.8	Haft bright
Requirement to be turned off	<0.8	Weak bright

To establish the health-diagnosis model of PBNNA, this study measures 600 training pairs of eight measurement parameters by using three vibration, three temperature, electrical voltage, and current sensors. Among the 600 training pairs of eight measurement parameters, there were 200 normal data, 200 abnormal data, and 200 data of required-to-be-turned-off. According to Equation (6), the leading eigenvalues greater than 0.5 for a covariance matrix of 600 training pairs are obtained, such as 277.16, 28.94, 22.94, 20.01, and 2.93. Accordingly, this study utilizes five principal components of 600 training pairs to establish a health-diagnosis model of PBNNA. By Equation (6), v₅ is obtained as $v_{5} = [\begin{matrix} 0.53 & - 0.43 & - 0.66 & - 0.30 & 0.02 \\ 0.53 & - 0.37 & 0.75 & - 0.16 & 0.01 \\ 0.53 & 0.82 & - 0.01 & - 0.22 & 0.02 \\ 0 & 0 & 0 & 0.06 & 0.97 \\ 0 & 0 & 0 & 0.01 & 0.21 \\ 0 & 0 & 0 & 0.01 & 0.13 \\ 0.40 & - 0.01 & - 0.09 & 0.91 & - 0.05 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}]$ (10)

As a result, the five principal components y₅ of 600 training pairs of eight measurement parameters are obtained by Equation (1). According to Equation (1), the first, second, ... , and eighth rows of v₅ are the five-principal-component contribution factors of the vibrations of the X, Y, and Z axes of the electromechanical system, the temperatures of the field winding, the shell of the electric motor generator, room temperature, electrical voltage, and current of the electromechanical system, respectively. Therefore, this study computes the contribution factor vector of five principal components from the sum of the elements in each row of v₅ divided by the sum of all elements of v₅, as shown as $v_{5 CF} = [\begin{matrix} 0.16 \\ 0.14 \\ 0.21 \\ 0.19 \\ 0.04 \\ 0.03 \\ 0.22 \\ 0 \end{matrix}]$ (11)

In Equation (11), the elements greater than 0.05 are in the first (0.16), second (0.14), third (0.21), forth (0.19), and seventh (0.22) entries. The results imply that the measurement parameters of the maximum five contribution factors of five principal components are the vibrations of the X, Y, and Z axes of the electromechanical system, the temperatures of the field winding, and the electrical voltage of the electromechanical system. Therefore, this study utilizes these five measurement parameters to establish a health-diagnosis model of PBNNA.

Eventually, this study utilizes 600 training pairs of eight measurement parameters to establish a health-diagnosis model for BNNA and PBNNA. According to the literature [31], the criteria for the hidden-neuron number, FN, of the neural network model with statistical errors is shown as $FN = \frac{4 {IP}^{2} + 3}{{IP}^{2} - 8}$ (12) where IP is the number of inputs. Therefore, this study utilizes 600 training pairs to obtain a two-layer network based on five neurons in the hidden layer with a hyperbolic tangent sigmoid transfer function and one neuron in the second layer with a linear transfer function for eight inputs of the vibrations of the X, Y, and Z axes of the electromechanical system, the temperatures of the field winding, the shell of the electric motor generator, room temperature, electrical voltage, and current of the electromechanical system; and one output of the conditions of normal, abnormal, and required-to-be-turned-off system states by using Equation (12) and BNNA, as shown in Fig. 5. Moreover, 600 training pairs are utilized to obtain a two-layer network based on six neurons in the hidden layer with a hyperbolic tangent sigmoid transfer function and one neuron in the second layer with a linear transfer function for five inputs of the vibrations of the X, Y, and Z axes of the electromechanical system, the temperatures of the field winding, the electrical voltage of the electromechanical system, and one output of the normal, abnormal, and requirement to be turned off the electromechanical system states using Equation (12) and PBNNA, as shown in Fig. 6. This study assumes that the target values of one, two, and three are the conditions at normal, abnormal, and required-to-be-turned-off states, respectively. Eventually, this study utilizes MATLAB to establish the BNNA and PBNNA models by using the initial conditions μ = 0.005 and minimum performance gradient of 1 × 10^-7. Consequently, the models of BNNA and PBNNA are established owing to μ = 500 and a performance gradient of 8.62 × 10^-8 based on 156 iterations, for μ = 500 a performance gradient of 9.93 × 10^-8 based on 668 iterations, respectively. The best training performances of the mean squared error based on the BNNA and PBNNA models are 2.23 × 10^-12 and 4.46 × 10^-12, as shown in Figs. 7 and 8, respectively.

Fig. 5

Two-layer network based on five neurons in the hidden layer and one neuron in second layer for eight inputs of the vibrations of X, Y, and Z axes of electromechanical system, the temperatures of the field winding, the shell of electric motor generator, room temperature, electrical voltage, and current of electromechanical system, and one output of the conditions of normal, abnormal, and required-to-be-turned-off states by using the BNNA.

Fig. 6

Two-layer network based on six neurons in hidden layer and one neuron in second layer for five inputs of the vibrations of X, Y, and Z axes of electromechanical system, the temperatures of the field winding, and electrical voltage of electromechanical system, and one output of the conditions of normal, abnormal, and required–to-be-turned-off states by using the PBNNA.

Fig. 7

Training performance of mean squared error based on BNNA.

In Figs. 7 and 8, the blue line represents the training performance, and the red line is the testing performance based on 600 training pairs of the same training data.

Fig. 8

Training performance of mean squared error based on PBNNA.

To verify the BNNA and PBNNA models, this study utilizes 300 pairs of measurement parameters that are not in the training database to test these two models. Among the 300 pairs of measurement parameters, there are 100 normal data, 100 abnormal data, and 100 to-be-turned-off data. The accuracy rates based on BNNA and PBNNA models were obtained as 97.7% and 98%, respectively. Although this study uses the PBNNA model with only 5 inputs, the test accuracy rate of the PBNNA model is slightly higher than that of the BNNA model with 8 inputs. Therefore, PBNNA successfully reduces the dimensionality of the multivariate dataset, as hypothesized. The two-layer network of the PBNNA model in Fig. 6 represents a suitable model for the health-diagnosis of the electromechanical system.

5 Experiment

To represent the automatic experiment of health-diagnosis of the electromechanical system, this study utilizes a single-chip multiprocessor (Arduino Mega) based on PBNNA to diagnose the states of the electromechanical system and upload the measurement-analysis results to the cloud website server. In this study, a free ThingSpeak ™ platform service was utilized for the cloud website server. This study utilizes an external braking device to provide different load states to simulate the operating state of the electromechanical system under normal, abnormal, and required-to-be turned-off conditions of power generation. Figure 9 represents normal, abnormal, and required-to-be-turned-off states of power generation. In addition, the single-chip multiprocessor based on PBNNA automatically and synchronously uploads the measurement and diagnosis results to the Thing Speak ™ platform service, as shown in Fig. 10. Figure 10 (a) depicts the real-time eight measurement results of the vibrations of the X, Y, and Z axes of the electromechanical system, the temperatures of the field winding, the shell of the electric motor generator, the room temperature, the electrical voltage, and the current of the electromechanical system. Figure 10 (b) represents the health-diagnosis result of the electromechanical system. In Fig. 10 (b), the values of one, two, and three are the conditions at normal, abnormal, and required-to-be-turned-off system states, respectively.

Fig. 9

Photos of (a) normal, (b) abnormal, (c) required-to-be-turned-off, and (d) return-to-normal states of power generation.

Fig. 10

(a) Real-time eight measurement results of the vibrations of X, Y, and Z axes, the temperatures of the field winding, the shell of electric motor generator, room temperature, electrical voltage, and current, and (b) health-diagnosis result of the electromechanical system.

Initially, this study controls the motor rotating speed of 1217 rpm without a load to generate 1.9 W to power the light bulb for a normal condition of power generation, which is the result value of one in Fig. 10 (b), as shown in Fig. 9 (a). Second, this study utilizes an external braking device to provide a load of 0.41 Nm to generate 0.8 W to power the light bulb for an abnormal condition of power generation, which is the result value of two in Fig. 10 (b), as shown in Fig. 9 (b). Third, this study utilizes an external braking device to provide a load of 1.21 Nm to generate 0.7 W to power the light bulb for a required-to-be-turned-off condition of power generation, which is the result value of three in Fig. 10 (b), as shown in Fig. 9 (c). In this state, the light bulb is weakly lighted, which implies that the electromechanical system is in a dangerous running state and must be turned off. Finally, this study removes the load on electromechanical system and returns to the motor rotating speed of 1220 rpm to generate 1.9 W to power the light bulb for a normal condition of power generation, which is the result value of one in Fig. 10 (b), as shown in Fig. 9 (d). Therefore, according to the results of Figs. 9 and 10, this study successfully diagnoses normal, abnormal, and required-to-be-turned-off states by PBNNA.

6 Conclusion

This study has established a cloud tele-measurement technique on an electromechanical system based on a PBNNA to quickly diagnose its performance. In this study, three vibration, three temperature, electrical voltage, and current sensors were mounted on the electromechanical motor, and the external braking device was used to provide different load states to simulate the operating states of the motor under different conditions. Moreover, the single-chip multiprocessor is used through the sensor to instantly measure the vibration, temperature, and electrical characteristics of the running motor. To quickly diagnose the operating states of the electromechanical system, this study classifies them as normal, abnormal, and required-to-be-turned-off states by PBNNA. Furthermore, PBNNA successfully reduces the dimensionality of the multivariate dataset, allowing for quick analysis of the electromechanical system’s performance. The accuracy rates of health-diagnosis based on BNNA and PBNNA models were obtained as 97.7% and 98%, respectively. Although this study uses the PBNNA model with only 5 inputs, the test accuracy rate of the PBNNA model is slightly higher than that of the BNNA model with 8 inputs. Finally, a single-chip multiprocessor based on PBNNA is used to automatically upload the measurement and analysis results of the electromechanical system to the cloud website server, so that the monitoring person can obtain the remote diagnosis of the electromechanical system. Therefore, this study could be employed in the electromechanical system to reduce equipment risks, to greatly increase the production rate of equipment, and to achieve intelligent manufacturing in light-off factories in the future.

Footnotes

Acknowledgments

The authors wish to thank National Science Council of Taiwan for financial supports (grant numbers: 108–2221-E-019–056).

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Health-diagnosis of electromechanical system with a principal-component bayesian neural network algorithm

Abstract

Keywords

1 Introduction

2 Tele-measurement structure of electromechanical system

Table 1 Conditions of normal, abnormal, and required-to-be-turned-off states Item Electrical power (W) Light-bulb state Normal ≥1.8 and <10 Full bright Abnormal ≥0.8 and <1.8 Haft bright Requirement to be turned off <0.8 Weak bright

Footnotes

Acknowledgments

References

Table 1
Conditions of normal, abnormal, and required-to-be-turned-off states

Item Electrical power (W) Light-bulb state

Normal ≥1.8 and <10 Full bright

Abnormal ≥0.8 and <1.8 Haft bright

Requirement to be turned off <0.8 Weak bright