## 3 Cutting-Edge Online Fault Diagnosis Techniques for Al-Caps
### Signal-Based Online Fault Diagnosis Techniques (SB-ON-FDTs)  
In [27], the authors introduced an SB-ON-FDT to assess the condition of the al-cap used in the output filter of a forward converter. They established an analytical relationship between two features, of the capacitor's voltage ripple and current ripple signals, namely,  
Figure 2: Simplified equivalent circuit of an al-cap [14]. the peak-to-peak values of these waveforms. It was later demonstrated that the previous analytical relationship could be equally applied to buck-type converters operating in both continuous conduction mode (CCM) and discontinuous conduction mode (DCM) [28]. It is important, however, to emphasize that the previous relationship is only valid in a steady state regime, which means that load variations are not considered. Later, in [29], the authors proposed an SB-ON-FDT for boost and buck-boost converters, based on a novel analytical relationship between the output voltage ripple and the input current. The key advantage of this approach is that it eliminates the need for a current sensor in the capacitor branch. In [30], the authors present an analytical relationship between the average power dissipated by the capacitor and the root mean square (RMS) value of its current to estimate the ESR. This solution was integrated into a pulse-width modulation (PWM) adjustable speed drive (ASD). The methods outlined above first extract features from the signals using time-domain techniques. Afterwards, a straightforward analytical relationship is used to estimate the ESR value and, finally, using the ESR value, it is possible to evaluate the al-cap's condition. The approaches described below can be also categorized as SB-ON-FDTs. However, instead of applying time-domain techniques to extract signal features, they employ frequency-domain techniques. In [31], the authors present a solution for estimating the ESR value based on a simple relationship between the fundamental components of the capacitor's voltage and those of its current. To implement this solution, an intelligent, cost-effective, and straightforward electronic module was designed for a DC-DC forward converter which provides an alert when the al-cap needs replacement. Specifically, when the estimated ESR value exceeds twice that of a sound capacitor, replacement is advised. Subsequently, the same principle was applied to an ATX power supply to assess primary side condition of al-caps [32]. Unlike the solution proposed in [31], which combines a bandpass filter with a (root mean square) RMS to DC converter to estimate the ESR, in [32], the discrete Fourier transform (DFT) algorithm is used to estimate the ESR at the converter's switching frequency. Subsequently, in [33], the Goertzel algorithm is applied to the DC-link capacitors used in front-end rectifier-fed three-phase inverters to extract the waveform characteristics of the capacitor's current and voltage. Following this, using two analytical relationships between signal features, it is possible to estimate both the ESR and C. In [19], the authors combine the discrete wavelet transform (DWT) with an RMS filter and a Kalman filter to estimate the both the ESR and C values of the al-cap used in the output filter of a three-phase interleaved boost converter (3\(\upmu\)IBC). Subsequently, in [34], the ESR value is estimated by combining the Hilbert transform with two filters: an RMS and an average filter. This approach eliminates the need for a dedicated current sensor in the capacitor branch, as it uses the inductor currents that are required for 3\(\upmu\)IBC control. In [35], the authors also use the inductor current and output voltage ripple to estimate the ESR. After acquiring the signals from a buck converter, they apply empirical mode decomposition (EMD) followed by the Hilbert-Huang transform (HHT) to extract the signal's modes, from which the ESR value is estimated.