# Software for Monitoring the In-Service Efficiency of Hydraulic Pumps
## 4 The Laboratory Validation of the Software Module for the Pump's Full Operating Range
### Sensitivity Analysis of the Algorithm for Various Operating Points  
In some situations, particularly in situ, the input parameters in the software module cannot be precisely determined (e.g., the inner diameter of the line or the coefficient of longitudinal losses). This is why we have performed the sensitivity analysis of the output value (pump efficiency) in relation to the input values using the algorithm parameters. The variables that can influence the pump efficiency are: (1) input values read by the operator \(p_{s}\) [Pa] and \(p_{d}\) [Pa] and (2) the parameters of the algorithm corresponding to the in situ configuration, which are scanned from the unique barcode generated for each pump: (i) diameter of the line at suction/discharge \(D_{s/d}\) [m]; (ii) the discharge transducer's quota compared to the suction transducer's quota \(\Delta z_{d/s}\) [m]; (iii) the length of the line from suction/discharge up to the location of the pressure manometers (transducers) compared to the pump flanges \(l_{s/d}\) [m]; and (iv) the coefficient of longitudinal losses along the suction/discharge line \(\lambda_{s/d}\) [-]. To gain a more relevant view of how these parameters influence the pump's efficiency, the percentage variation of the pump efficiency has been represented in relation to the percentage variation of each input value. Moreover, to assess the sensitivity of the algorithm parameters for the pump's full range of operation, we have considered five operating points (OP8, OP9, OP10, OP12, OP14) from the range of flow rates corresponding to the defined areas  
One can notice the significant influence of the static pressure variation read at the pump discharge \(\epsilon_{p_{d}}\) on the pump efficiency. The operating points laid out in the vicinity of the maximum efficiency influence the pump efficiency within the limit \(\epsilon_{p_{p}}<\pm 12\%\) when the deviation of the static pressure determined at the pump discharge is read with a deviation within the limit \(\epsilon_{p_{d}}<\pm 25\%\). For the operating points laid out in the yellow and red zones, a slight deviation in the reading of the static pressure at the pump discharge \(\epsilon_{p_{d}}>\pm 5\%\) leads to deviations in the values of the pump efficiency greater than \(\epsilon_{p_{p}}>\pm 12\%\). For greater positive deviations at the reading of the static pressure at the pump discharge, an error message is returned because the input of the pressure difference between the pump suction and discharge is greater than the pumping head prescribed from the pump's catalog curve. Figure 9 shows the algorithm sensitivity analysis for the determination of pump efficiency for the percentage variation of static pressure \(e_{p_{s}}\) measured at the pump suction for the five operating points selected across the full range. One can notice a linear distribution of the pump efficiency variation, with the percentage variation of the static pressure \(\epsilon_{p_{s}}\) measured at the pump suction. As expected, the variation of the static pressure read at the pump suction \(e_{p_{s}}\) has a significant influence over the pump efficiency variation. The operating points located in the green area are an exception; the influence on the pump efficiency is less \(\epsilon_{p_{p}}<\pm 1\%\) when the variation of the static pressure determined at pump suction is read with a deviation within the limit of \(\epsilon_{p_{s}}<\pm 50\%\). Otherwise, for the operating points located in the yellow area, the pump variation can reach \(\epsilon_{p_{p}}<\pm 5\%\) when the variation of the static pressure taken at pump suction is read with a deviation within the limit of \(\epsilon_{p_{s}}<\pm 50\%\). Figure 8: Sensitivity analysis of the algorithm regarding the determination of the pump efficiency \(\epsilon_{p_{d}}\) for deviations in the reading of the discharge pressure \(\epsilon_{p_{d}}\) for five operating points: OP8, OP9, OP10, OP12 and OP14.