# Prediction Method of Soft Fault and Service Life of DC-DC-Converter Circuit Based on Improved Support Vector Machine

^{*}

## Abstract

**:**

## 1. Introduction

_{c}of the electrolytic capacitor was estimated. Specifically, X. Duan et al. [10] adopted a band-pass filter in order to process the acquired capacitive voltage and current to obtain ${R}_{c}$ and C

_{value}(capacity of capacitor) of the capacitor within a certain frequency range. However, the use of the filter has led to higher costs and slower parameter-detection rates. Tang et al. [11] established the Buck-converter model based on the hybrid-system theory and identified the capacitor’s characteristic parameters ${R}_{c}$ and C

_{value}by means of the least-square method. Yet, this method relies on the acquisition of inductive current, output voltage and switch-status signal, and raises requirements for the sampling rate of signals. Lu et al. [12] set up the Boost-converter hybrid-system model using the same method, and the problem of identifying the characteristic parameters of components was transformed into the problem of the global optimization of a multivariable fitness function where ${R}_{c}$ and C

_{value}were solved through an optimization algorithm. In [13,14], a fault-detection electronics scheme was applied to the insulated gate bipolar transistor (IGBT) by M. A Rodríguez-Blanco and Xinchang Li et al., which was based on online monitoring of the collector current slope signal during the turn-on transient. Sun et al. [15] investigated the application of single-input–single-output (SISO) and multiple-input–single-output (MISO) neural networks for the online monitoring of IGBTs. Moreover, Dusmez et al. [16,17] considered the inductive resistance, the R

_{c}of the electrolytic capacitor, and the drain-source on-resistance of a power MOSFET in the Boost converter and obtained the transfer-function model between the inductive current and the output voltage; the value of the on-resistance ${R}_{on}$ was then estimated online with the help of software-frequency-response analysis (SFRA). This method applies to circuits under the continuous conduction mode (CCM) and the discontinuous conduction mode (DCM), but it requires the detection of inductive current, and the value of the capacitance ${R}_{c}$ limits its applicability. Wu et al. [18] utilized the bond-graph theory for modeling the Boost converter in order to yield redundant parsing expressions, and the genetic algorithm was combined in order to identify the drain-source on-resistance ${R}_{on}$ of a power MOSFET. Sun et al. [19] set up the Boost-converter hybrid-system model based on the hybrid-system theory and capitalized on the particle-swarm-optimization algorithm to identify ${R}_{on}$, which achieved the simultaneous detection of the characteristic parameters of multiple components in the circuit but required a certain sampling frequency of circuit-detection signals. All the above methods revealed the performance status of a component by detecting the changes in its parameters, thus predicting the faults and service life of the system. Nevertheless, they failed to take an all-sided consideration of how the degradation of other components affects the performance of the DC–DC converter.

## 2. Fault Prediction Model

#### 2.1. Model Initialization

#### 2.2. Online Model Updates

- (1)
- Adding samples

- (2)
- Removing samples

#### 2.3. Adaptive Selection of the Sliding-Time-Window Length

#### 2.4. Optimized Computation of Model Parameters Based on DP-PSO

## 3. Simulation Experiments and Result Analyses

#### 3.1. Establishment of Degradation Models for Key Components

- (1)
- Performance-Degradation Model of Electrolytic Capacitor

_{value}(capacity of capacitor), is expressed as:

_{value}over time is expressed as:

- (2)
- Performance-Degradation Model of Power MOSFET

- (3)
- Performance-Degradation Model of Inductor

- (4)
- Performance-Degradation Model of Power Diode

#### 3.2. Selection of Characteristic Parameters for Circuit-Level Faults

#### 3.3. Determination of Parameters for the Prediction Model

#### 3.4. Testing of Prediction-Model Performance

- (1)
- Testing of the Prediction Efficiency of the Model

- (2)
- Testing of Prediction Accuracy of the Model

#### 3.5. Analysis of Simulation Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

DC–DC | Direct Current to Direct Current |

AONBLSSVM | Adaptive Online Non-bias Least-Square Support-Vector Machine |

DP-PSO | Double-Population Particle-Swarm Optimization |

OLS-SVM | Online Least-Square Support-Vector Machine |

MOSFET | Metal-Oxide-Semiconductor Field-Effect Transistor |

IGBT | Insulated Gate Bipolar Translator |

R_{c} | Equivalent-Series Resistance |

$\overline{{P}_{c}}$ | Average Power Loss of Capacitor |

I_{C} | Effective Value of Capacitive Current |

C_{value} | Capacity of Capacitor |

SISO | Single Input–Single Output |

MISO | Multiple Input–Single Output |

CCM | Continuous Conduction Mode |

DCM | Discontinuous Conduction Mode |

R_{on} | Drain-source On-resistance of Metal-Oxide-Semiconductor Field-Effect Transistor |

SVM | Support-Vector Machine |

LSSVM | Least-Square Support-Vector Machine |

ONBLSSVM | Online Non-bias Least-Square Support-Vector Machine |

KKT conditions | Karush–Kuhn–Tucker conditions |

C | Penalty Factor |

$\lambda $ | Introduced Parameter |

${\sigma}^{2}$ | Gaussian Kernel Function Breadth Factor |

$\theta $ | Prediction-Error Threshold |

$\epsilon $ | Refers to The Relative Decrement Threshold |

Vout | Output Voltage of Direct Current to Direct Current |

Pout | Output Power of Direct Current to Direct Current |

Upp | Ripple Voltage |

t | Time |

∆t | Time Interval |

MAD | Mean Average Deviation |

MAPE | Mean Average Percentage Error |

Theil IC | Theil’s Inequality Coefficient |

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Time | ESR/Ω | C/uF | RON/Ω | RD/Ω | L/uH | UPP/V |
---|---|---|---|---|---|---|

0 | 0.0200 | 1000.0000 | 0.0200 | 0.0100 | 33.00 | 0.092 |

1∆t | 0.0209 | 997.7493 | 0.0206 | 0.0101 | 32.56 | 0.098 |

2∆t | 0.0219 | 994.9920 | 0.0213 | 0.0103 | 32.12 | 0.106 |

3∆t | 0.0230 | 991.6141 | 0.0222 | 0.0105 | 31.68 | 0.112 |

4∆t | 0.0243 | 987.4759 | 0.0233 | 0.0108 | 31.24 | 0.120 |

5∆t | 0.0257 | 982.4064 | 0.0246 | 0.0112 | 30.80 | 0.138 |

6∆t | 0.0272 | 976.1958 | 0.0261 | 0.0118 | 30.36 | 0.147 |

7∆t | 0.0290 | 968.5874 | 0.0280 | 0.0126 | 29.92 | 0.161 |

8∆t | 0.0310 | 959.2666 | 0.0302 | 0.0139 | 29.48 | 0.173 |

9∆t | 0.0333 | 947.8479 | 0.0329 | 0.0156 | 29.04 | 0.198 |

10∆t | 0.0360 | 933.8591 | 0.0361 | 0.0180 | 28.60 | 0.236 |

11∆t | 0.0390 | 916.7219 | 0.0400 | 0.0215 | 28.16 | 0.263 |

12∆t | 0.0428 | 895.7276 | 0.0446 | 0.0264 | 27.72 | 0.291 |

13∆t | 0.0473 | 870.0080 | 0.0502 | 0.0334 | 27.28 | 0.350 |

14∆t | 0.0528 | 838.3950 | 0.0570 | 0.0433 | 26.84 | 0.433 |

15∆t | 0.0600 | 799.8997 | 0.0065 | 0.0574 | 26.40 | 0.546 |

AONBLSSVM Prediction Model | |||
---|---|---|---|

Experiment No. | MAD | MAPE (%) | Theil IC |

1 | 0.95 × 10^{−3} | 7.796 × 10^{−1} | 4.747 × 10^{−3} |

2 | 1.00 × 10^{−3} | 6.561 × 10^{−1} | 4.017 × 10^{−3} |

3 | 1.20 × 10^{−3} | 5.300 × 10^{−1} | 3.278 × 10^{−3} |

4 | 1.30 × 10^{−3} | 5.410 × 10^{−1} | 3.219 × 10^{−3} |

5 | 1.45 × 10^{−3} | 5.088 × 10^{−1} | 3.248 × 10^{−3} |

OLS-SVM Prediction Model | |||
---|---|---|---|

Experiment No. | MAD | MAPE (%) | Theil IC |

1 | 1.15 × 10^{−3} | 9.405 × 10^{−1} | 5.049 × 10^{−3} |

2 | 1.10 × 10^{−3} | 7.201 × 10^{−1} | 4.279 × 10^{−3} |

3 | 1.60 × 10^{−3} | 7.035 × 10^{−1} | 4.197 × 10^{−3} |

4 | 1.65 × 10^{−3} | 6.867 × 10^{−1} | 3.879 × 10^{−3} |

5 | 1.90 × 10^{−3} | 6.655 × 10^{−1} | 3.912 × 10^{−3} |

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**MDPI and ACS Style**

Hou, Y.; Wu, Z.; Cai, X.; Dong, Z.
Prediction Method of Soft Fault and Service Life of DC-DC-Converter Circuit Based on Improved Support Vector Machine. *Entropy* **2022**, *24*, 402.
https://doi.org/10.3390/e24030402

**AMA Style**

Hou Y, Wu Z, Cai X, Dong Z.
Prediction Method of Soft Fault and Service Life of DC-DC-Converter Circuit Based on Improved Support Vector Machine. *Entropy*. 2022; 24(3):402.
https://doi.org/10.3390/e24030402

**Chicago/Turabian Style**

Hou, Yuntao, Zequan Wu, Xiaohua Cai, and Zhongge Dong.
2022. "Prediction Method of Soft Fault and Service Life of DC-DC-Converter Circuit Based on Improved Support Vector Machine" *Entropy* 24, no. 3: 402.
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