Residual-Based Leak Detection and Severity Monitoring Using a PLC-Embedded Neural Observer for a Coupled-Tank System

2.1 Coupled-tank system description

For experimental validation, a real-time Quanser coupled-tank system was used to investigate nonlinear level dynamics, hydraulic coupling, and leak-monitoring performance. As shown in Figure 1, the platform includes vertically connected upper and lower tanks, a variable-speed pump, level sensors, a Siemens S7-1200 PLC, an HMI, an SM1234 analog input/output (I/O) module, and a VoltPAQ-X1 signal-conditioning interface. Water is pumped to the upper tank and then flows to the lower tank through the interconnecting path, producing coupled nonlinear behavior. Both tank levels are continuously measured and transmitted to the PLC.

Figure 1. Real-time Quanser coupled-tank systems (CTS) experimental platform

Within this platform, the PLC performs cascade PI control, signal acquisition, neural-observer inference, residual evaluation, and leak-monitoring logic. The HMI displays the measured and estimated levels, control variables, residuals, and alarm states. Dedicated upper- and lower-tank leak ports were used to introduce controlled disturbances and assess the ability of the proposed PLC-resident framework to distinguish persistent leakage from normal closed-loop operation. From an automation perspective, control and diagnostic functions are executed as separate PLC tasks while using common process signals. The 50 ms control loop remains solely responsible for pump actuation, whereas the 500 ms monitoring task updates residuals, alarm status, leak location, and severity for HMI supervision. Hence, diagnostic processing does not interfere with the control action. Moreover, all monitoring calculations are performed within the PLC, avoiding reliance on external asynchronous computation.

2.2 PLC-based residual monitoring architecture

Figure 2 illustrates the PLC-based architecture used to integrate cascade-level control, neural-level prediction, and residual-based leak monitoring for the coupled-tank platform described in Section 2.1. The Siemens S7-1200 PLC performs two coordinated functions: a cascade PI control layer for closed-loop level regulation and a residual monitoring layer for leak assessment. Importantly, the monitoring function operates in parallel with the control task and does not modify the underlying control structure. The coupled-tank process operates in continuous time, where ${{h}_{u}}$(t) and ${{h}_{l}}$(t) denote the upper- and lower-tank liquid levels, respectively. After signal conditioning and analog acquisition, the level measurements are sampled by the PLC and represented in discrete time as

${{h}_{u}}\left( k \right)={{h}_{u}}\left( k{{T}_{s}} \right)$                           (1)

${{h}_{l}}\left( k \right)={{h}_{l}}\left( k{{T}_{s}} \right)$                               (2)

where, T_s is the sampling period and k is the discrete-time index. The PLC-generated pump command u_i(k) is converted through the analog output interface to drive the pump. Accordingly, the hydraulic behavior of the coupled-tank process can be expressed using mass-balance relationships:

 ${{A}_{u}}\frac{d{{h}_{u}}\left( t \right)}{dt}={{q}_{p}}\left( t \right)-{{q}_{ul}}\left( t \right)-{{q}_{Lu}}\left( t \right)$                    (3)

${{A}_{l}}\frac{d{{h}_{l}}\left( t \right)}{dt}={{q}_{ul}}\left( t \right)-{{q}_{o}}\left( t \right)-{{q}_{Ll}}\left( t \right)$                          (4)

where, A_u and A_l are the cross-sectional areas of the upper and lower tanks, respectively; q_p(t) is the pump inflow; q_ul(t) is the inter-tank flow; and q_o(t) is the lower-tank outlet flow. The terms q_Lu(t) and q_Ll(t) represent leak flows from the upper and lower tanks. For gravity-driven flow through a small leak opening, the leak flows are represented by

${{q}_{Lu}}\left( t \right)={{C}_{d}}{{a}_{Lu}}\sqrt{2g{{h}_{u}}\left( t \right)}$                     (5)

${{q}_{Ll}}\left( t \right)={{C}_{d}}{{a}_{Ll}}\sqrt{2g{{h}_{l}}\left( t \right)}$                               (6)

where, C_d is the discharge coefficient, g is the gravitational acceleration, and a_Lu and a_Ll are the equivalent leak areas. Under normal operation, these terms are negligible. By contrast, when a controlled leak is introduced, the additional level-dependent outflow changes the nominal hydraulic response and causes deviations between the measured and predicted tank levels. In the cascade PI layer, the outer loop regulates the lower-tank level according to the reference h_sp(k). The outer-loop error is given by

${{e}_{o}}\left( k \right)={{h}_{sp}}\left( k \right)-{{h}_{l}}\left( k \right)$                        (7)

The outer PI controller generates the intermediate reference u_o(k) for the upper tank. The inner-loop error is then calculated as

${{e}_{i}}\left( k \right)={{u}_{o}}\left( k \right)-{{h}_{u}}\left( k \right)$                    (8)

The inner PI controller produces the pump command u_i(k). This cascade arrangement regulates the lower-tank level while accounting for the coupled hydraulic response of the upper tank. Meanwhile, the residual-monitoring layer receives buffered process and control variables from the PLC. To ensure causal execution and temporal alignment, the neural observer uses closed-loop variables from the preceding monitoring instant. The observer input vector is therefore defined as:

$x\left( k-1 \right)={{\left[ {{e}_{o}}\left( k-1 \right){{e}_{i}}\left( k-1 \right){{u}_{o}}\left( k-1 \right){{u}_{i}}\left( k-1 \right) \right]}^{T}}$                     (9)

Figure 2. PLC-based residual monitoring architecture for the coupled-tank system

After normalization using the stored training parameters, the delayed input vector is processed by the PLC-embedded MLP to generate the one-step-ahead nominal tank-level estimates at the current monitoring instant:

$\hat{h}\left( k|k-1 \right)={{f}_{MLP}}\left( x\left( k-1 \right)\text{; }\!\!\Theta\!\!\text{ } \right)$                (10)

where, Θ denotes the stored MLP weights and biases. The notation $\hat{h}$(k|k–1) indicates that the tank levels at monitoring instant k are predicted using information available at instant k−1. For compactness, $\hat{h}$(k|k–1) is denoted by $\hat{h}$(k) hereafter. The observer output is expressed as:

$\hat{h}(k)=\left[\hat{h}_u(k) \hat{h}_l(k)\right]^T$                      (11)

where, ${{\hat{h}}_{u}}\left( k \right)$ and ${{\hat{h}}_{l}}\left( k \right)$ are the predicted upper- and lower-tank levels, respectively. The detailed MLP structure, model selection, training procedure, and PLC deployment are presented in Sections 2.3–2.5. Based on these estimates, the measured and predicted levels are compared to generate the residual vector:

$r\left( k \right)=h\left( k \right)-\hat{h}\left( k|k-1 \right)$                                  (12)

where

$h\left( k \right)={{\left[ {{h}_{u}}\left( k \right){{h}_{l}}\left( k \right) \right]}^{T}}$                        (13)

and

$r\left( k \right)={{\left[ {{r}_{u}}\left( k \right){{r}_{l}}\left( k \right) \right]}^{T}}$                     (14)

Thus, the individual residuals are obtained as

$r_u(k)=h_u(k)-\hat{h}_u(k \mid k-1)$                  (15)

  ${{r}_{l}}\left( k \right)={{h}_{l}}( k )-{{\hat{{h}}\,}_{l}}\left( k|k-1 \right)$                (16)

where, r_u(k) and r_l(k) are the residuals associated with the upper and lower tanks, respectively. During leak-free operation, the MLP estimates both tank levels with limited mismatch, whereas leakage introduces sustained residual deviations through additional outflow. The monitoring logic therefore evaluates filtered residuals against baseline thresholds under stable conditions and confirms persistent exceedance over a prescribed interval. After confirmation, residual magnitude determines severity, while the calibrated two-channel signature indicates the leak location on the HMI.

2.3 Lightweight multilayer perceptron neural observer design

The neural observer is implemented as a lightweight MLP to estimate the nominal upper- and lower-tank levels during closed-loop operation. Instead of directly classifying leaks, it generates nominal level estimates for residual calculation. A compact architecture is adopted to preserve deterministic PLC execution alongside signal acquisition, cascade PI control, residual processing, and HMI communication. As shown in Figure 3, the network comprises an input layer, two hidden layers, and an output layer, with the general configuration expressed as

$M:{{n}_{x}}-{{n}_{h1}}-{{n}_{h2}}-{{n}_{y}}$                   (17)

where, n_x, n_h1, n_h2, and n_y denote the numbers of neurons in the input, first hidden, second hidden, and output layers, respectively. In this work, n_x = 4 corresponds to the closed-loop variables {e_o(k–1), e_i(k–1), u_o(k–1), u_i(k–1)}, whereas n_y = 2 represents the predicted upper- and lower-tank levels. The hidden-layer dimensions are evaluated during the offline model-selection procedure in Section 2.4. Within this formulation, for each network layer, the pre-activation vector and layer output are calculated as

 ${{z}^{\left( j \right)}}\left( k \right)={{W}^{\left( j \right)}}{{a}^{\left( j-1 \right)}}\left( k \right)+{{b}^{\left( j \right)}}$                  (18)

${{a}^{\left( j \right)}}\left( k \right)=\phi \left( {{z}^{\left( j \right)}}\left( k \right) \right)$                (19)

where, W^(j) and b^(j) are the weight matrix and bias vector of layer j, respectively. The vector z^(j)(k) represents the weighted-sum, or pre-activation, vector formed from the output of the preceding layer.

Figure 3. Lightweight multilayer perceptron (MLP) neural observer architecture

The vector a^(j)(k) denotes the output of layer j, and ϕ(⋅) is the activation function. Hyperbolic tangent activation is applied in the hidden layers to represent the nonlinear relation between the closed-loop variables and the coupled-tank levels. The input to the first hidden layer is defined as:

${{a}^{\left( 0 \right)}}\left( k \right)={{x}_{n}}\left( k \right)$                 (20)

where, x_n(k) is the normalized observer input. Each input variable is normalized using the statistics obtained from the normal training data:

${{x}_{n,i}}\left( k \right)=\frac{{{x}_{i}}\left( k \right)-{{\mu }_{x,i}}}{{{\sigma }_{x,i}}},i\in \left\{ 1,...{{n}_{x}} \right\}$                    (21)

where, x_i(k) is the i-th input variable, while μ_x,i and σ_x,i are its corresponding mean and standard deviation. Because the observer performs continuous level estimation, the output layer uses a linear activation function. The normalized predicted-level vector is obtained as:

${{\hat{h}}_{n}}\left( k \right)={{W}^{\left( 3 \right)}}{{a}^{\left( 2 \right)}}\left( k \right)+{{b}^{\left( 3 \right)}}$                   (22)

where, W⁽³⁾ and b⁽³⁾ are the output-layer weights and biases. The predicted values are then converted to physical level units as:

${{\hat{h}}_{i}}\left( k \right)={{\hat{h}}_{n,i}}\left( k \right){{\sigma }_{h,i}}+{{\mu }_{h,i}},i\in \left\{ u,~l \right\}$                         (23)

where, μ_h,i and σ_h,i are the output normalization parameters for the corresponding tank level. Accordingly, the total number of trainable parameters is:

${{N}_{p}}=\left( {{n}_{x}}+1 \right){{n}_{h1}}+\left( {{n}_{h1}}+1 \right){{n}_{h2}}+\left( {{n}_{h2}}+1 \right){{n}_{y}}$                (24)

Based on these considerations, the final architecture was selected based on prediction accuracy, nominal residual variation, parameter count, and PLC implementation feasibility. The resulting estimates, ${{\hat{h}}_{u}}\left( k \right)$ and ${{\hat{h}}_{l}}\left( k \right)$, were then used for residual generation and subsequent leak detection, location indication, and severity classification.

2.4 Offline training and model selection

Offline training was performed using leak-free closed-loop data collected from the physical Quanser CTS. The lower-tank reference alternated between 13 and 17 cm every 200 s for 10 cycles. PLC variables were logged via Modbus TCP at 250 ms and downsampled to the 500-ms monitoring interval. Each input–target pair consisted of x(k−1) and h(k), separated by one monitoring interval. To preserve temporal separation and prevent data leakage, complete set-point segments were divided into training, validation, and test sets in proportions of approximately 70%, 15%, and 15%, respectively. Moreover, inputs and targets were standardized using statistics obtained exclusively from the training set. All models used tanh hidden layers, a linear output layer, Adam optimization (η = 0.001, L₂ = 10⁻⁴), a batch size of 512, and 200 training epochs. The validation set was used for architecture selection, whereas the test set was reserved for final evaluation.

For architecture comparison, four lightweight MLP configurations were considered: 4–4–4–2, 4–6–4–2, 4–6–6–2, and 4–8–8–2. These structures provided increasing representation capacity while remaining suitable for PLC implementation. Their performance was assessed using root mean square error (RMSE), mean absolute error (MAE), residual standard deviation (SD), coefficient of determination, parameter count, multiply–accumulate (MAC) count, nominal-trial alarm flags, false alarm rate (FAR) and PLC execution time.

$RMS{{E}_{i}}=\sqrt{\frac{1}{N}\mathop{\sum }_{k=1}^{N}{{\left( {{h}_{i}}\left( k \right)-{{{\hat{h}}}_{i}}\left( k \right) \right)}^{2}}}$                 (25)

$MA{{E}_{i}}=\frac{1}{N}\mathop{\sum }_{k=1}^{N}\left| {{h}_{i}}\left( k \right)-{{{\hat{h}}}_{i}}\left( k \right) \right|$                     (26)

${{\sigma }_{r,i}}=\sqrt{\frac{1}{N-1}\mathop{\sum }_{k=1}^{N}{{\left( {{r}_{i}}\left( k \right)-{{{\bar{r}}}_{i}} \right)}^{2}}}$                   (27)

$R_{i}^{2}=1-\frac{\mathop{\sum }_{k=1}^{N}{{\left( {{h}_{i}}\left( k \right)-{{{\hat{h}}}_{i}}\left( k \right) \right)}^{2}}}{\mathop{\sum }_{k=1}^{N}{{\left( {{h}_{i}}\left( k \right)-{{{\bar{h}}}_{i}} \right)}^{2}}}$                          (28)

where, i ∈ {u, l}, N is the number of testing samples, h_i(k) and ${{\hat{h}}_{i}}\left( k \right)$ are the measured and predicted levels, respectively, r_i(k) is the residual, ${{\bar{r}}_{i}}$ is the mean residual, and ${{\bar{h}}_{i}}$ is the mean measured level. RMSE and MAE characterize the magnitude of the prediction error, whereas σ_r,i describes the dispersion of the nominal residual and is therefore relevant to threshold stability and leak sensitivity. The coefficient $R_{i}^{2}$ indicates how well the estimated trajectory follows the measured level over the evaluated operating range. Accordingly, the observer architecture was selected by considering prediction accuracy, nominal residual behavior, model size, and practical PLC deployment requirements rather than relying on a single performance index.

Table 1. Validation performance and PLC-oriented screening of candidate multilayer perceptron (MLP) observers

(a) Prediction performance

(b) PLC-oriented implementation screening

To evaluate the complete PLC-resident framework, the proposed monitoring scheme was assessed on the physical Quanser coupled-tank platform. The Siemens S7-1200 PLC executed cascade PI control at T_c = 50 ms and performed neural estimation, residual analysis, alarm confirmation, leak-location indication, and severity assessment at T_m = 500 ms. Meanwhile, process data were recorded through Modbus TCP at 250 ms for subsequent metric calculation and figure preparation. Importantly, all control and leak-decision functions were completed online in the PLC.

4.1 Experimental setup and leak-test conditions

The test bench comprised the Quanser coupled-tank process, VoltPAQ-X1 interface, Siemens S7-1200 PLC, SM1234 analog I/O module, and HMI. For real-time supervision, Figure 5 shows the monitoring interface used to display measured and estimated levels, residual signals, thresholds, alarm status, indicated leak location, and severity class.

Figure 5. Real-time PLC monitoring human–machine interface (HMI)

Prior to validation, the selected 4–6–4–2 MLP was trained on leak-free 13–17 cm data, after which its weights, biases, and normalization parameters were fixed in the PLC. Subsequently, tests were conducted at lower-tank setpoints of 13 and 17 cm, representing two calibrated hydraulic operating regions. The reported performance is therefore bounded to these setpoints, the stated controller and sensor configuration, and one controlled leak at a time. Accordingly, the results should not be extrapolated as evidence of unchanged accuracy over the full tank range. Controlled upper- and lower-tank leaks were introduced using the grooved plug in Figure 6, with Small (S), Medium (M), and Large (L) conditions defined by 2, 3, and 4 screw turns, respectively. Each test comprised nominal operation, leak initiation, and sustained leakage. Table 2 summarizes the leak classes and measured flow ranges, while Table 3 lists the PLC monitoring parameters. Section 4.7 states the data and recalibration required for other operating regions.

Figure 6. Adjustable grooved leak plug

Table 2. Leak conditions and measured leak-flow ranges

Table 3. Common PLC monitoring and decision parameters.

For hydraulic characterization, leak-flow ranges in Table 2 were obtained from QL = 60ΔV/Δt. Each leak condition was repeated three times at 13 and 17 cm for hydraulic analysis and calibration of the residual signatures and severity boundaries. To maintain separation between calibration and testing, these trials were excluded from the event-level dataset, in which each of the seven classes was tested ten times per operating point. With T_m = 500 ms, T_confirm = 2.0 s corresponded to four consecutive monitoring cycles. Notably, T_log was used only for data recording, while g(k) was selected from h_sp ∈ {13, 17} cm.

4.2 Nominal observer tracking and transient rejection

To examine nominal tracking under transient operation, Figure 7 presents a representative leak-free reference change from 17 to 13 cm. This case was selected because it produced the larger closed-loop deviation and therefore provided a demanding assessment of nominal prediction and transient rejection. As shown in Figure 7(a), the upper- and lower-tank levels responded at different rates because of cascade control and hydraulic coupling, while the PLC estimates, ${{{\hat{h}}}_{{u}}}( {k} )$ and ${{{\hat{h}}}_{{l}}}({k})$, reproduced the main trends and converged toward the new operating condition. Despite this agreement, temporary measured–predicted deviations occurred during the rapid response, particularly in the upper-tank channel.

(a) level tracking

(b) stable-condition verification

Figure 7. Representative nominal 17-to-13 cm transition

More importantly, Figure 7(b) shows how stable-condition verification prevented these nominal deviations from triggering false alarms. Immediately after the setpoint change, |∣Δh_sp∣ exceeded ε_h, while the control action caused repeated ∣Δu_i∣ excursions beyond ε_u. Consequently, St(k) became false, and residual-based decisions were inhibited throughout the transient interval. Monitoring was considered continuously stable only after approximately 50.5 s, when both conditions remained satisfied.

For clarity, the shaded regions in Figure 7 indicate the initial stable period, rejected transient interval, and restored stable condition. Taken together, the results show that reference-induced level and residual excursions were rejected as normal closed-loop transients rather than interpreted as leakage. Once stability was restored, residual evaluation and baseline adaptation resumed, while EMA filtering and persistence confirmation further suppressed short-duration threshold crossings. Similarly, the reverse 13-to-17 cm transition exhibited comparable behavior; however, the 17-to-13 cm case is presented because it produced the larger transient deviation. The 17-to-13 cm and reverse 13-to-17 cm steps provided the available sudden-reference tests, producing both controller action and residual excursions. During these transients, the stability gate suspended alarm accumulation and baseline adaptation until the setpoint and pump-command variations returned within their limits. Normal sensor noise was inherently included in the baseline statistics, whereas no additional noise injection or independent pump-voltage disturbance was applied. Therefore, robustness to prescribed noise levels, pump degradation, supply disturbances, and simultaneous setpoint/leak events remains outside the present validation scope.

4.3 Closed-loop hydraulic responses under controlled leakage

Following the nominal transient assessment, Figures 8 and 9 present representative measured-level responses at h_sp= 17 cm. For comparison across operating regions, the same seven operating conditions were also tested at 13 cm. However, only the 17 cm results are shown to avoid repetitive figures. Nevertheless, results from both operating points are used subsequently for residual calibration and performance evaluation. The leak was introduced at approximately 17 s while the cascade PI controller remained active. During the initial nominal interval, before leak initiation, all measured responses remained within narrow nominal bands. After leak initiation, Figure 8 shows that an upper-tank leak directly reduced h_u because the additional outflow occurred before the inter-tank flow path. The reduction increased with leak severity. In contrast, a lower-tank leak reduced the regulated lower-tank level and caused the outer PI controller to increase the upper-tank reference and pump command. Consequently, h_u increased above its nominal value. Thus, the opposing response directions result from the disturbance location and the compensating action of the cascade controller. Consistent with the upper-tank behavior, Figure 9 shows the corresponding lower-tank responses. A lower-tank leak directly reduced h_l below the reference before the controller restored the required inter-tank inflow. Conversely, for an upper-tank leak, the controller compensated for the upstream loss by increasing the pump command. Under the applied controller tuning, this compensation produced a temporary positive deviation in h_l before the level returned toward its reference. For both leak locations, larger screw openings resulted in greater deviations and stronger recovery actions.

Figure 8. Upper-tank level responses under controlled leakage at h_sp = 17 cm

Figure 9. Lower-tank level responses under controlled leakage at h_sp = 17 cm

To quantify these responses, for each condition, RMSE, integral absolute error (IAE) and maximum absolute deviation were averaged over three post-leak trials using the unfiltered 250 ms data. Across the evaluated conditions, as shown in Figure 10, all indices increased with leak severity. Lower-tank leaks produced the largest h_u deviations because the outer PI controller increased the upstream level to compensate for the loss, whereas h_l deviations remained smaller due to direct level regulation.

Figure 10. Measured-level deviation indices under controlled leakage at h_sp= 17 cm

Although the leak conditions appear distinguishable in Figures 8 and 9, the measured levels alone do not provide a robust online alarm variable. These figures compare synchronized experiments with a known leak-onset time and an available leak-free reference, whereas the PLC observes only the current process trajectory. Moreover, the nominal reference transition in Section 4.2 produces level excursions that may exceed those associated with a Small leak. In addition, feedback compensation can also restore h_l close to its reference despite persistent leakage. Consequently, a fixed threshold applied directly to h_u or h_l would be sensitive to the operating point, normal transients, hydraulic coupling, and controller action.

To overcome these limitations, the MLP observer is used to estimate the nominal upper- and lower-tank levels, ${{\hat{h}}_{u}}$ and ${{\hat{h}}_{l}}$, from the closed-loop variables e_o, e_i, u_o, and u_i. Accordingly, these estimates represent the expected leak-free behavior of the controlled process. The residuals ${{r}_{u}}={{h}_{u}}-{{\hat{h}}_{u}}$ and ${{r}_{l}}={{h}_{l}}-{{\hat{h}}_{l}}$ then quantify the deviation of the measured levels from their nominal predictions. Therefore, compared with direct thresholding of h_u and h_l, the residuals provide a more consistent basis for transient rejection, adaptive thresholding, leak-location indication, and severity classification at both 13 and 17 cm.

4.4 Residual responses, leak separability and threshold calibration

Following the measured-level responses in Section 4.3, the observer residuals were examined as leak-sensitive features for the PLC decision layer. For illustration, Figures 11 and 12 show representative responses at h_sp = 17 cm. The thin traces denote the raw signed residuals r_u and r_l, whereas the thicker traces represent the corresponding EMA-filtered residuals r_s,u and r_s,l. Under nominal conditions, before leak initiation, both channels remained near their nominal baselines. After leak initiation, the filtered signals developed sustained responses whose magnitudes increased from Small to Medium and Large conditions. For decision purposes, the signed residuals were retained for location interpretation, whereas leak detection and severity assessment used the filtered magnitude residuals r_f,u, r_f,l and r_sev defined in Eqs. (30) and (46). In particular, upper-tank leaks produced a negative upper residual and a dominant positive lower residual, whereas lower-tank leaks showed the opposite pattern. Accordingly, because hydraulic coupling and cascade-controller compensation affected both channels, leak location was determined from the combined residual directions and relative magnitudes rather than from the largest residual alone.

Figure 11. PLC-generated raw and signed exponential moving average (EMA) residual responses for upper-tank leaks at h_sp = 17 cm

Figure 12. PLC-generated raw and signed exponential moving average (EMA) residual responses for lower-tank leaks at h_sp = 17 cm

Based on these residual patterns, Table 4 summarizes the calibrated location signatures and severity boundaries for the 13 and 17 cm operating regions. For each region g ∈ {13, 17}, the six leak classes: Upper-S, Upper-M, Upper-L, Lower-S, Lower-M, and Lower-L, were repeated three times, yielding 18 calibration events. Importantly, these trials were conducted separately from the event-level performance dataset.

For each calibration event e, the EMA-filtered residual features were evaluated over a steady post-confirmation interval. Specifically, the interval was selected after alarm confirmation, while stable operation was maintained and the residuals showed no sustained growth or decay. Because settling behavior varied among leak conditions, the interval was determined separately for each event; however, the same procedure and number of consecutive samples were used throughout. Accordingly, the event signature was calculated as

${{\bar{q}}_{e}}=\frac{1}{{{N}_{e}}}\mathop{\sum }_{k={{k}_{1,e}}}^{{{k}_{2,e}}}{{\left[ {{r}_{s,u}}\left( k \right){{r}_{s,l}}\left( k \right){{r}_{f,u}}\left( k \right){{r}_{f,l}}\left( k \right) \right]}^{T}}$                  (49)

where, k_1,e and k_2,e define the steady post-confirmation interval and N_e = k_2,e − k_1,e +1 is the number of monitoring samples in that interval.

Table 4. Calibrated residual-signature parameters and severity boundaries at 13 and 17 cm

After event-level signatures were obtained, the prototype vectors c_U,g and c_L,g were obtained by averaging the event signatures of the corresponding upper- and lower-tank calibration trials within operating region g. To avoid class imbalance, the three severity classes and their three repetitions were assigned equal weight. Thus, each prototype represented the overall residual response of its corresponding leak location rather than that of a single severity condition. Initially, equal nominal importance was assigned to the four residual features. Subsequently, differences in their natural variation were accounted for using the diagonal inverse-variance scaling matrix

${{W}_{g}}=diag\left[ \frac{1}{\sigma _{1,g}^{2}},~\frac{1}{\sigma _{2,g}^{2}},~\frac{1}{\sigma _{3,g}^{2}},~\frac{1}{\sigma _{4,g}^{2}} \right]$                     (50) 

where, $\text{ }\!\!\sigma\!\!\text{ }_{\text{j,g}}^{\text{2}}$ denotes the variance of feature j obtained from the calibration event signatures in operating region g. As a result, this normalization prevents features with greater dispersion from disproportionately influencing the signature-distance calculation without manually emphasizing a particular residual channel.

For each calibration event, the peak value of r_sev(k) was extracted over the selected steady interval. The representative severity residual p_sev,c,ℓ,g was calculated as the arithmetic mean of the three event peaks for severity class c ∈ {S, M, L}, leak location ℓ ∈ {U, L}, and operating region g ∈ {13, 17}. Finally, the severity boundaries were defined as the midpoints between adjacent representative class values:

$\text{T}{{\text{H}}_{S,\ell ,g}}=\frac{{{p}_{\text{sev},S,\ell ,g}}+{{p}_{sev,M,\ell ,g}}}{2}$                  (51)

$\text{T}{{\text{H}}_{M,\ell ,g}}=\frac{{{p}_{sev,M,\ell ,g}}+{{p}_{sev,L,\ell ,g}}}{2}$                (52)

To ensure an unbiased evaluation, all prototype vectors, scaling matrices, and severity boundaries were obtained exclusively from the calibration trials and were fixed before the 140 repeated event-level tests. Therefore, no calibration parameter was adjusted using the test confusion matrices or alarm-delay results.

4.5 Representative PLC detection sequences and repeated-event performance

After fixing all calibration parameters, the PLC monitoring framework was evaluated at h_sp = 13 and 17 cm using ten trials for each of seven classes, giving 70 trials per operating point and 140 trials in total. Throughout each trial, neural inference, residual processing, threshold evaluation, confirmation timing, location indication, and severity classification were executed online in the PLC. Figures 13 and 14 present four representative detection sequences. In these figures, the green, yellow, and red regions indicate normal, candidate, and confirmed leak states, respectively. Specifically, the alarm delay consists of the threshold-crossing time, t_cross, followed by T_confirm = 2.0 s. At 17 cm, the Lower-M and Upper-L leaks were confirmed after 4.5 and 4.0 s, while at 13 cm, the Lower-L and Upper-S leaks were detected after 5.0 and 4.0 s. Overall, persistent residual deviations were confirmed within a few seconds while cascade control remained active. Beyond these representative cases, Table 5 reports the class-level results and PLC alarm delays. Delay statistics were calculated from correctly classified location–severity events, while an additional summary used all true-positive detections to avoid conditioning the overall delay on classification success. Across all true-positive detections, the mean alarm delay was 4.57 ± 0.71 s at 17 cm and 4.83 ± 0.84 s at 13 cm, based on 56 and 55 confirmed events, respectively. By comparison, the 99 events with correct location and severity labels yielded 4.46 ± 0.57 s and 4.80 ± 0.73 s. Thus, restricting the analysis to exactly classified events introduced only limited delay-selection bias. As expected, larger leaks were detected faster because their residuals developed more rapidly, whereas lower-tank leaks at 13 cm generally required longer detection due to the lower hydraulic head and cascade-controller compensation. To summarize the overall classification performance, Figure 15 presents the seven-class confusion matrices. Across both operating points, 111 of 120 leak trials were confirmed, while 19 of 20 Normal trials remained alarm-free. Accordingly, leak sensitivity, specificity, and binary accuracy were 92.50%, 95.00%, and 92.86%, respectively. Among the confirmed leaks, 103 were assigned to the correct tank and 101 to the correct severity class, giving conditional location and severity accuracies of 92.79% and 90.99%. For end-to-end evaluation, the nine missed leaks were counted as failures, resulting in location and severity accuracies of 103/120 = 85.83% and 101/120 = 84.17%. Moreover, 99/120 = 82.50% received both correct labels. Finally, including the 19 correctly identified Normal trials, the exact seven-class accuracy was 118/140 = 84.29%.

(a) lower-tank medium leak

(b) upper-tank large leak

Figure 13. Representative PLC detection sequences at h_sp = 17 cm

(a) lower-tank large leak

(b) upper-tank small leak

Figure 14. Representative PLC detection sequences at h_sp = 13 cm

Table 5. Event-level detection and classification counts with associated PLC alarm delays

(a) h_sp = 17 cm

(b) h_sp = 13 cm

Figure 15. Seven-class confusion matrices obtained from repeated PLC leak tests

The reported metrics use different denominators. Conditional location and severity accuracies are based on the 111 detected leaks, whereas end-to-end metrics include all 120 leak trials and treat the nine missed detections as failures, reducing the corresponding accuracies by 6.96 and 6.82 percentage points. Moreover, most remaining errors occurred for weaker Small/Medium leaks and at 13 cm, where residual separation was reduced by lower hydraulic head and cascade compensation. The exact seven-class metric is more stringent because a prediction is counted as correct only when the Normal/leak decision and, for leak cases, both location and severity match the applied class.

4.6 Discussion and comparison with representative diagnosis approaches

As a baseline comparison, measurement- and threshold-based monitoring provides a simple and computationally inexpensive solution for leak indication [23-25, 38]. However, the results in Figures 7-9 show that direct thresholds applied to tank levels, control errors, or controller outputs are not invariant under the present closed-loop conditions. Specifically, nominal reference changes produce temporary level excursions, whereas cascade PI compensation can return the regulated lower-tank level toward its reference despite sustained leakage. Moreover, hydraulic coupling also causes upper- and lower-tank leaks to influence both measured channels. Therefore, a threshold selected for weak-leak sensitivity may become susceptible to normal transients, while a wider threshold may fail to detect small residual changes.

To mitigate these effects, the proposed framework addresses this limitation by separating nominal-response estimation from alarm evaluation. Within this framework, the MLP observer generates the expected leak-free trajectories from e_o(k–1), e_i(k–1), u_o(k–1), and u_i(k–1), and the PLC rule layer evaluates the remaining measured–predicted mismatch. Subsequently, EMA filtering and adaptive baseline thresholds reduce noise and nominal drift, while stable-condition verification and confirmation timing suppress short transient crossings. After confirmation, the calibrated two-channel residual signature is used for location indication, and the filtered residual magnitude is compared with operating-region-dependent severity boundaries. The repeated experiments achieved a binary leak/no-leak accuracy of 92.86%. Among confirmed leaks, the conditional location and severity accuracies were 92.79% and 90.99%, respectively. When evaluated over all 120 leak trials, including unconfirmed events as failures, the corresponding end-to-end accuracies were 85.83% and 84.17%, while 82.50% received both correct location and severity labels.

The proposed approach also differs from direct data-driven classifiers. Edge-PLC and embedded ANN studies have demonstrated that learned models can operate close to the industrial control layer [20-22], while ANN and deep-learning methods can capture complex leak patterns from labeled pressure, acoustic, or time-series data [29, 31-35]. In comparison, as summarized in Table 6, these approaches offer strong pattern-recognition capability but generally require representative fault datasets and provide less transparent alarm decisions. In the present framework, the neural network is used only to reconstruct the nominal leak-free response, whereas detection, confirmation, location, and severity assessment remain within explicit PLC logic. As a result, this separation reduces dependence on extensive labeled leak data and allows the thresholds, timers, residual signatures, and severity boundaries to be inspected through the PLC program and HMI. Table 6 also contrasts the proposed framework with nonlinear observer-based diagnosis. High-gain observers provide an established basis for nonlinear state estimation [39], whereas Kalman-filter, dual-observer, and neuro-fuzzy observer methods support model-based residual generation, fault estimation, and uncertainty treatment [40-42]. These approaches provide strong theoretical interpretation but generally require an explicit process model, reliable hydraulic parameters, and additional observer or covariance tuning. In contrast, the proposed neural observer reduces this modeling burden by learning the nominal closed-loop response from experimental data while retaining the measured-versus-predicted residual interpretation commonly used in observer-based diagnosis.

Table 6. Positioning against representative leak- and fault-diagnosis approaches

From an implementation perspective, the multi-rate structure separates the 50 ms cascade-control task from the 500 ms monitoring task, while the 250 ms Modbus TCP stream is used only for data logging and figure preparation. For a fair comparison, the parameters and decision thresholds of the two baseline methods were determined from the available nominal/calibration data and were fixed before evaluation on the 140 repeated-event trials. No threshold was adjusted using the final test results. All three strategies were implemented using PLC-compatible logic and evaluated under the same experimental conditions. Within this architecture, Table 7 compares the proposed method with two PLC-compatible baseline methods using results from the same 140 experimental trials conducted on the physical coupled-tank testbed. Direct level-deviation thresholding has the lowest computational cost but yields the lowest binary accuracy and the highest false-alarm rate. Using MLP-2 with a fixed residual threshold improves detection performance, whereas the proposed adaptive residual logic further reduces false alarms and achieves the highest binary accuracy with only a modest increase in execution time.

Table 7. Same-dataset comparison of PLC-compatible leak-detection strategies