## 3 Results  
To demonstrate the effectiveness of detecting and isolating individual multiplicative amplifier faults, the amplifier parameters were deliberately and abruptly altered (one at a time) at the midpoint of the recording interval using relay cards (Figure 3). In this experimental setup, two parameter estimation approaches were developed. The first approach can be described as offline. Signal data were collected in the LabVIEW environment and stored as text files. The estimation process was then carried out in batch mode using MATLAB 2020b, where the estimation algorithm was implemented through dedicated m-files. Figure 7 presents a portion of the LabVIEW block diagram for generating and recording signals under multiplicative fault conditions. It illustrates the generation of the amplifier's input signal \(U_{\mathrm{c}}\), using a PRBS (Pseudo-Random Binary Sequence) and the measurement of the amplifier's output signal \(U_{\mathrm{m}}\). The system also enables monitoring of the armature voltage \(U_{\mathrm{a}}\), the armature current \(I_{\mathrm{a}}\) (by monitoring the voltage on the series resistor \(R_{\mathrm{d}}\), Figures 2b and 7), and the motor speed \(n\). Figure 8 presents a portion of the LabVIEW Block Diagram, which activates specific amplifier parameters by switching the corresponding relays, thereby inducing individual multiplicative faults. Figure 9 shows the Front Panel of the LabVIEW program used for monitoring input-output signals, featuring controls for the abrupt changing of one of the amplifier's parameter values in the event of a multiplicative fault. The software is configured so that all parameters are set to their nominal values (slider position 1) pri  
Figure 8: A segment of the LabVIEW Block Diagram developed to inject multiplicative faults into the system. Figure 7: A segment of the LabVIEW Block Diagram developed for generating and recording signals under multiplicative fault conditions. fault. At the fault moment, one of the amplifier parameters is changed. In the example shown, the resistance \(R_{12}\) is in 10 s reduced from its nominal value of 10 k\(\Omega\) to a lower value of 5.6 k\(\Omega\) (slider position 3) by automatically activating the corresponding relay. The second approach to detecting multiplicative faults in the amplifier and DC motor was developed entirely within the LabVIEW environment and can be classified as a real-time method. After acquiring the input-output signals (Figures 7 and 9) during the injection of specific multiplicative faults using relays (Figures 8 and 9), the signals are passed to the next frame of the Flat Sequence structure. Within this structure, the desired estimation algorithm, either discrete (SWA), based on (14)-(16), or continuous (SIA), based on (30) and (31), is implemented using a MathScript Node within the LabVIEW software (Figure 10). The estimated parameters of the amplifier \(b_{0d}\), \(b_{1d}\), and \(a_{1d}\) from the discrete model of the amplifier (8) (SWA), or \(b_{0}\), \(b_{1}\), and \(a_{1}\) from the continuous model of the amplifier (6) (SIA), are then displayed in the Chart block of the LabVIEW program. Figure 11 displays section of the LabVIEW Front Panel displaying the estimation of continuous parameters \(b_{0}\), \(b_{1}\), and \(a_{1}\) using the SIA. Figure 10: LabVIEW MathScript Node for SIA-based parameter estimation. Figure 9: LabVIEW Front Panel for acquisition of input-output signals under multiplicative fault conditions. The procedure for generating multiplicative motor faults, specifically changes in inductance (\(L\)), armature resistance (\(R_{\text{a}}\)), moment of inertia (\(J\)), and viscous friction coefficient (\(B\)), was implemented at the simulation level using the Multisim environment.