Lambda-Guided Bounded Scale Adaptation for A Physics-Guided Virtual Mass-Airflow Estimator: A BMW M30B35 Simulation Stud y

Here m ̇^fuel,k is the reconstructed fuel flow: m ̇~air,k= m ̇^fuel,kAFRstλk. (2) In the implementation, the current reconstructed fuel flow is multiplied by the measured lambda, delayed by 22 samples (0.44 s) and passed through a first-order low-pass filter with a 0.12 s time IJEMT constant (α = 1/7 at 50 Hz). The frozen estimator output undergoes the same delay and filtering before candidate fitting and acceptance. Lambda already includes the simulated exhaust and sensor dynamics, so this extra conditioning does not remove bias or transient misalignment. Calibration is disabled for the first 40 samples (0.80 s), allowing 22 samples for the delay and 18 for filter settling. Four-stage supervisor. The online estimate is m ̇^ = sφk, where m ̇^ is the committed airflow, φk is the frozen network output and s∈[0.80,1.20]. Table 3 lists the fixed calibration settings. – Stage A, validity. Simulator health flags exclude cold operation, fuel cut, enrichment, injector saturation, invalid lambda, misfire, dropout, stuck signals and observer warm-up. Measured coolant temperature must be at least 60 °C, and |dTPS/dt| must be at most 400 % s−1. Invalid samples are skipped. Valid samples already stored in the proposal and acceptance buffers are retained across these gaps. An invalid sample while a proposal is being formed resets the 60- sample excitation buffer. The health-flag interface is assumed in the simulation; a physical fault detector was not implemented or tested. – Stage B, excitation. Consider the approximate model zk= sφk+ vk, where zk is the pseudo- reference airflow and vk is zero-mean Gaussian noise. The sensitivity to the scale s is φk. Accumulating the squared sensitivity over a window W gives the scalar Fisher-information- inspired score Is(W) = 1 σpseudo 2 ∑φk 2 k∈W ≥Is,min. (3) The excitation buffer holds Nw= 60 consecutive valid samples. With σpseudo 2 = 0.64 and Is,min= 104, the threshold corresponds to an RMS airflow of √Is,min σpseudo 2 Nw = 10.3gs−1. The threshold was selected using the threshold-selection runs and remained fixed thereafter. Because filtering introduces correlation and the pseudo-reference contains bias, Eq. (3) serves as a fixed excitation score rather than a calibrated uncertainty measure. – Stage C, proposal. The least-squares candidate is scand= ∑φk k m ̇~k∑φk 2 k ⁄ . A deadband of 0.002 suppresses small changes. The candidate step is limited to ±0.02, the scale to [0.80, 1.20] and its rate to 0.01s−1, using the time elapsed since the last commit. The candidate remains separate from the scale used for inference until the acceptance decision. Each proposal and acceptance buffer must span at least 8 s and hold at least two valid samples. The excitation test uses the latest 60 consecutive valid samples when the proposal decision is made. C1 and C2 follow the same later-window schedule but accept every bounded candidate, skipping only the improvement test. The Stage D improvement-test column in Table 4 records this distinction; all online policies use only information available up to the decision time. – Stage D, acceptance. The candidate is evaluated on a later window Wa that holds Na valid samples and spans at least 8 s. The acceptance and proposal windows do not overlap. Its mean- squared error against the conditioned pseudo-reference is L(s; Wa) = 1 Na ∑[m ̇~air,k−sφk] 2 k∈Wa , (4) The pseudo-reference is defined by Eq. (2). Hidden airflow is used only for offline evaluation. IJEMT The candidate scand replaces the last-known-good scale sLKG only if the relative error falls by at least 2%: ρ= L(sLKG; Wa) −L(scand; Wa) max[L(sLKG; Wa), ε] ≥ρmin= 0.02, (5) Here ε = 10−9 (g s−1)2 prevents division by zero. If ρ< 0.02, the update is rejected and sLKG is kept. Fig. 2 shows the separate proposal, acceptance and final-holdout windows. The holdout contributes no samples to candidate fitting or acceptance. C5 uses scalar recursive least squares with a forgetting factor of 0.985 and the same scale and rate limits. It updates without an excitation gate, a later-window acceptance test or rollback. Recursive least squares has also been proposed for correcting physics-model factors against sensor calibration drift (Imafidon, 2026). False-update labels are assigned offline. An accepted update is false if its acceptance-window RMSE against identically delayed and filtered hidden airflow is more than 1.5 g s−1 above the RMSE of the previous scale. The false-update rate is the proportion of accepted updates that meet this degradation criterion. The label describes degradation within the acceptance window and does not measure failure in the final holdout. C5 has no discrete acceptance events, so it has no comparable label. Fig. 2. Calibration and final evaluation windows. Table 3. Calibration settings. Parameter Value Parameter Value Initial scale / bounds 1.0; [0.80, 1.20] Gate window / threshold 60 samples; 10 000 Per-update / rate limit 0.02; 0.01 s−1 Pseudo-reference variance 0.64 (g s−1)2 Deadband 0.002 Minimum improvement 2% Proposal / acceptance 8 s / 8 s Offline false-update limit 1.5 g s−1 2.3 Experimental Design and Statistics The original final-test evaluation used predeclared criteria. The high-load fault test was designed after inspecting those results and is reported separately as exploratory. IJEMT E1–E4 evaluate frozen estimators under nominal conditions, boundary and corner conditions, unseen transients and plant mismatch. E5 compares the six policies in Table 4 on 12 untouched calibration-shift runs and five network seeds, yielding 60 run–seed pairs for each policy. Each run contains an adaptation segment followed by a holdout segment evaluated with the final scale frozen. The secondary calibration-data efficiency experiment (E6) is reported in the GitHub repository. Table 4. Calibration policies. Mode Description Stage A Excitation gate Stage D improvement test Online policy C0 Frozen residual AI – – – Yes C1 Bounded adaptation without validity checks No No No Yes C2 Validity-only adaptation Yes No No Yes C3 Four-stage supervisor Yes Yes Yes Yes C4 True-airflow benchmark Yes No Yes No C5 Scalar RLS Yes No No Yes Policies marked “Online policy” do not use hidden airflow as feedback. Policies C2, C3 and C5 also assume the simulated health interface; C1 omits the validity check. C4 uses hidden airflow in both proposal and acceptance, so it serves only as a simulation benchmark. The metrics are mean absolute error , root-mean-square error and normalised RMSE : MAE= 1 n∑|y^k−yk| k , (6) RMSE= √ 1 n∑(y^k−yk)2 k , (7) NRMSE= RMSE 260gs−1, (8) Here yk is the reference airflow, y^k is the estimated airflow and n is the number of samples. NRMSE uses a fixed reporting span of 260 g s−1 to keep the normalisation identical across runs and policies. This denominator is not the standard deviation or a range estimated separately for each run. Signed bias and the 95th-percentile absolute error are also reported. Metrics were first computed for each run–seed pair and then averaged over seeds within each run. Statistical inference used independent runs as the units of observation; time samples and network seeds were not treated as independent replicates. Paired differences were checked with the Shapiro–Wilk test, followed by a paired t-test or a Wilcoxon signed-rank test. The analysis uses 5000-resample bootstrap intervals, paired Cohen’s dz (the mean difference divided by its standard deviation) and Holm correction across six planned comparisons. The acceptance criteria were fixed before the final test was inspected: C3 NRMSE ≤0.12, at least 10% improvement over C0, no scale-bound violations and a false-update rate strictly lower than C1. The six planned comparisons were recalculated after seed averaging and restricted to the 12 IJEMT final-test calibration runs. The archived statistical_tests.csv pooled threshold-selection and final- test runs and was excluded from the p-values reported here. Nominal accuracy uses 5000- resample bootstraps over independent runs, with seed 0. The GitHub repository documents the corresponding correction to the E6 analysis. Exploratory fault test. The protocol was written after inspection of the original final-test results and was not externally preregistered. The first execution files could not be recovered. All exploratory results reported here come from one re-run implemented from the written protocol. The configuration was locked before inspection of the output (SHA-256 prefix f18aa3b6206b3978); settings remained unchanged. The test used twelve new 240 s high-load trajectories with seeds 2026100400–2026100411. All 12 trajectories were employed for each feedback condition as well as five frozen network seeds, resulting in 60 run–seed pairs for each policy. These trajectories adopted the same plant and sensor-noise models as before with severe VE mismatch added at 80 seconds. The commands were kept inside of the typical training parameters of 3400– 4400 RPM and 60–78% TPS. The seven matched conditions included those with healthy feedback and had faults in the range of 15% with some faults being brief, others recurring, and some faults being persistent, in the range of 80–88 s, 80–160 s respectively. Almost every fault was arranged in blocks of 8 s on and 8 s off, either in synchrony with the proposal windows or with a random phase, sampled independently for each run. Dropout, stuck-signal and misfire events have been disabled to verify the lambda corruption only is the problem. Networks, controller thresholds and bounds were kept constant. The configurations and results can be found in the GitHub data repository provided in Data and code availability. The primary exploration objective was RMSE of the committed estimation of the full 80 s adaptation period with noise obtained using unfiltered hidden airflow. The secondary outcomes were holdout NRMSE and original false update label. The average of 5 network seeds was taken in each run. In each condition, two-sided exact sign-flip tests were done in each comparison for C3 versus C1, C2 and C5 where α = 0.05 and Holm correction applied for 21 comparisons. This assumes that there is equality under the null in run-level difference. The average number of run-bootstrap resamples (seed 0) used to obtain the unadjusted 95% percentile interval is 5000. No negative or zero feedback was removed no matter the results. However, there has been no change in the acceptance criteria or endpoint for the original 12-run calibration experiment, the primary confirmatory analysis, as a result of the exploratory fault test. 3. Results 3.1 Estimator Accuracy Nominal accuracy. On 10 untouched 90 s runs, residual AI reduced MAE from 1.453 to 0.438 g s−1. The reductions relative to speed density and pure AI were 69.9% and 3.95%, respectively (Table 5). No separate paired test was predeclared for nominal conditions. Across all 94 matched test trajectories, residual AI had lower NRMSE than pure AI: mean difference −0.0097, pHolm= 4.6 × 10−12 and dz= −0.43 (Table 10). IJEMT Table 5. Nominal accuracy: means [95% bootstrap CIs], 10 runs. Model MAE (g s−1) RMSE (g s−1) NRMSE P95 error (g s−1) Physics-only 1.453 [1.014, 1.975] 1.895 [1.397, 2.455] 0.00729 3.820 Pure AI 0.456 [0.404, 0.509] 0.590 [0.529, 0.655] 0.00227 1.194 Residual AI 0.438 [0.386, 0.491] 0.573 [0.510, 0.637] 0.00220 1.166 Transients. The twelve unseen 120 s runs cover seven operating states (Table 6). Residual AI achieved an MAE of 0.319 ± 0.022gs−1, compared with 0.434 ± 0.072 for pure AI and 0.889 g s−1 for speed density. These correspond to MAE reductions of 26.6% relative to pure AI and 64.2% relative to speed density. Residual AI had the lowest MAE in six of the seven states. Pure AI had slightly lower MAE during acceleration (0.340 versus 0.345 g s−1). Cross-correlation analysis detected no lag at the 20 ms sampling resolution. Fig. 3 shows one representative run. Table 6. Transient MAE (g s−1), averaged over 12 runs and five network seeds. Estimator Idle Tip-in Accel. Cruise High load Tip-out Decel. Physics-only 0.372 0.308 0.899 0.936 1.497 1.097 0.643 Pure AI 0.300 0.169 0.340 0.398 0.699 0.756 0.410 Residual AI 0.113 0.124 0.345 0.383 0.447 0.457 0.224 Fig. 3. Airflow estimates during an unseen transient run. Boundary and corner conditions. Residual AI achieved the lowest MAE in five of the eleven conditions excluded from training, but speed density had lower pooled MAE in both groups (Table 7). Each group contains 10 runs and 30 000 samples, with the AI results averaged over five seeds. The seed standard deviation of corner MAE was 1.9 g s−1 for residual AI and 17.0 for pure AI. The physical baseline reduced variation between seeds, although the residual model remained unreliable outside its training coverage. Practical use would require a validated fallback to the physics estimate. IJEMT Table 7. Boundary and corner MAE (g s−1); best values are bold. Group Condition Physics Pure AI Residual AI Boundary Minimum-speed idle 0.407 1.036 0.170 Redline 13.326 3.602 17.264 Wide-open throttle 1.064 7.037 3.625 Minimum MAP 1.809 1.726 1.642 Extreme intake temperature 0.494 0.315 0.290 Extreme coolant temperature 0.719 23.919 3.331 Pooled 2.970 6.272 4.387 Corner Lugging 1.164 0.555 0.238 Engine braking 1.534 16.326 6.749 Cold high load 2.395 19.255 4.316 Hot wide-open throttle 1.381 19.370 5.890 Redline, low MAP 5.229 38.910 3.705 Pooled 2.340 18.883 4.180 Plant mismatch. Plant mismatch was evaluated with the estimators held fixed: 10 runs each covered nominal, low and high VE mismatch, and six each covered MAP-gain and manifold- time-constant error. Table 8 lists NRMSE for the nominal, VE-mismatch and MAP-gain conditions. At low VE mismatch (scale 1.06 and +150 rpm shift), residual AI improved on speed density but had slightly higher NRMSE than pure AI. At high mismatch (scale 0.90 and −300 rpm shift), speed density reached 0.01068, residual AI 0.01250 and pure AI 0.01267. Residual AI was then 17.1% worse than speed density. Linear interpolation between the 6% and 10% VE-mismatch cases places the NRMSE crossover near 8.8% for both networks (8.6% using MAE). Both the VE scale and surface shape differed, so this is a descriptive estimate rather than a validated operating limit (Fig. 4). Residual AI had the lowest NRMSE under MAP-gain error. With a slower manifold, pure AI had slightly lower NRMSE, while residual AI had lower MAE. The plant-mismatch result files in the GitHub repository listed under Data and code availability provide that comparison. Table 8. NRMSE under plant mismatch; best values are bold. Estimator Nominal Low VE High VE MAP gain Physics-only 0.00729 0.01234 0.01068 0.00578 Pure AI 0.00227 0.00769 0.01267 0.00599 Residual AI 0.00220 0.00786 0.01250 0.00544 IJEMT Fig. 4. NRMSE under VE mismatch. 3.2 Pseudo-Reference Quality The conditioned pseudo-reference was compared with identically delayed and filtered hidden airflow using the coefficient of determination Rpseudo 2 over the calibration-eligible samples, with the conditioned hidden airflow as the reference. Hidden airflow is excluded from the online calibration path. The pseudo-reference tracked the conditioned airflow closely: R2 = 0.9940 ± 0.0010 on eight threshold-selection runs and 0.9939 ± 0.0007 on 12 final-test runs, with individual values of 0.9922–0.9953. Its final-test bias was +1.25 ± 0.18gs−1, about 3.5% of mean airflow, and arose from the imposed injector mismatch. The close agreement in trend therefore coexisted with a systematic calibration bias. A bounded, single-scale model limits adaptation, but later-window acceptance cannot identify a bias that both windows shares. 3.3 Excitation Gate Behaviour The excitation gate blocked no proposal in the calibration-shift runs: the smallest proposal score was 13 397, above the 10 000 thresholds. The 15 rejected final-test updates failed the later- window improvement test. Fig. 5 shows scale changes, excitation and decisions in one shift run; the GitHub repository provides the detailed logs. On eight steady-idle trajectories replayed with five frozen networks, no complete 60-sample window passed the excitation gate. The mean and maximum scores were 745 and 789, both below 8% of the threshold, at a mean hidden airflow of 2.76 g s−1. In contrast, every tested window in final-test shift run 000 passed. Overlapping windows describe gate behaviour and are not independent statistical observations. The replay records are available in the GitHub repository. IJEMT Fig. 5. Scale, the excitation score defined by Eq. (3) and update decisions during a shift run. Steady idle was the only low-information condition tested. With one scale parameter, the excitation score is a sum of squared airflow, and therefore functions mainly as a minimum- airflow criterion. The replay shows that the gate rejects sustained idle and admits one shift trajectory. These results provide no evidence of protection against a biased pseudo-reference that still meets the excitation criterion. The single-parameter test also cannot establish identifiability for a model with several adjustable parameters. 3.4 Calibration-Policy Ablation Table 9 compares post-shift holdout performance over the 12 final-test runs. C3, the four-stage supervisor, reduced mean NRMSE from 0.01522 for C0 to 0.00789 (48.2%) and MAE from 3.374 to 1.633 g s−1. The paired t-test gave t(11) = −8.269 with 11 degrees of freedom, raw p= 4.8 × 10−6, pHolm= 2.4 × 10−5 and dz= −2.39. The committed scale remained within its bounds. C3 accepted 203 proposals and rejected 15. Table 9. Post-shift holdout accuracy (mean ± SD; 12 runs). Mode NRMSE MAE (g s−1) C0 0.0152 ± 0.0023 3.374 ± 0.548 C1 0.0071 ± 0.0019 1.450 ± 0.433 C2 0.0079 ± 0.0036 1.629 ± 0.842 C3 0.0079 ± 0.0036 1.633 ± 0.844 C4 0.0048 ± 0.0042 0.972 ± 0.951 C5 0.0083 ± 0.0035 1.727 ± 0.833 (b) Scalar excitation score Is IJEMT Table 9 (continued). Final scale (mean ± SD) and events (60 run–seed pairs). Mode Final s Accepted/rejected Incomplete candidates False acc. C0 1.000 ± 0.000 0/0 0 – C1 0.950 ± 0.011 238/0 43 0 C2 0.954 ± 0.018 218/0 38 0 C3 0.954 ± 0.018 203/15 34 0 C4 0.931 ± 0.022 220/0 30 0 C5 0.957 ± 0.018 – – – C4 uses true airflow and is a simulation benchmark that cannot be deployed. C5 is continuous RLS and has no discrete acceptance or false-update labels. “Rejected” means the improvement test failed; “incomplete” means adaptation ended before acceptance finished. Both retain the previous scale. The false-update counts for C3 and C1 were 0/203 and 0/238 accepted updates. First acceptance occurred at 16.02 s, about 800 continuously valid samples; 55 of 60 pairs updated under C2–C4. The GitHub repository provides the sample-budget analysis and event totals. C3 did not differ significantly from C1, C2 or C5 in the planned paired tests (Table 10). The mean NRMSE difference relative to C2 was 2 × 10−5; relative to RLS, mean NRMSE was 4.7% lower. These tests do not show that the policies are equivalent. C1 had the lowest deployable mean, largely because of stuck-sensor run 002. C1 accepted four corrupted-feedback updates on this run, whereas C2–C5 did not update. The resulting improvement for C1 does not establish the reliability of adaptation without validity checks (see the sensitivity analysis in the GitHub repository). With run 002 removed, the mean NRMSE of C3 was 0.00698 instead of 0.00789. The differences remained nonsignificant: C3–C1 +2 × 10−5 (Wilcoxon p= 0.84), C3–C2 +2 × 10−5 (p= 0.81), and C3–C5 −4.2 × 10−4 (p= 0.58). Table 10. Paired NRMSE differences (first minus second); negative favours the first. Comparison Test n Mean diff. Residual AI vs. physics Wilcoxon 94 +0.00031 Residual AI vs. pure AI Wilcoxon 94 −0.00972 C3 vs. C0 paired t 12 −0.00733 C3 vs. C1 Wilcoxon 12 +0.00078 C3 vs. C2 Wilcoxon 12 +0.00002 C3 vs. C5 paired t 12 −0.00039 IJEMT Table 10 (continued). Holm-adjusted p-values and paired effect sizes. Comparison pHolm dz Residual AI vs. physics 1.000 +0.06 Residual AI vs. pure AI 4.6 × 10−12 −0.43 C3 vs. C0 2.4 × 10−5 −2.39 C3 vs. C1 1.000 +0.30 C3 vs. C2 1.000 +0.09 C3 vs. C5 1.000 −0.13 C3 met the predeclared accuracy, improvement and scale-bound criteria. It failed the requirement for a lower false-update rate than C1, because both rates were zero (Table 11). The overall predeclared outcome was therefore FAIL. No accepted update exceeded the specified hidden- error tolerance, so this label could not separate the policies. The result establishes neither a safety benefit nor the redundancy of the acceptance gate. Table 11. Predeclared acceptance criteria. Criterion Threshold Outcome C3 final-test NRMSE ≤0.12 Pass (0.00789) Improvement over C0 ≥10% Pass (48.2%) Scale-bound violations 0 Pass (0) C3 false-update rate lower than C1 Fail (0.000 vs. 0.000, tie) 3.5 Exploratory Adverse Calibration Test This exploratory re-run followed inspection of the original final-test results and does not replace that evaluation. All 2520 policy replays completed successfully, and the frozen-input checks confirmed that engine inputs and hidden airflow were identical across lambda conditions. Only the measured lambda and its pseudo-reference changed. C0 and the benchmark C4 were not affected by lambda faults. Every adaptation sample passed Stage A, and every C3 proposal passed the excitation gate. The experiment thus evaluates the later-window acceptance test under conditions where the other gates do not restrict proposals. The RMS airflow of the frozen estimate was 84.2–88.0 g s−1. At this high load, the existing 1.5 g s−1 false-update threshold is responsive: a scale change can alter window RMSE by at most |Δs| RMS(φ). With a maximum step of 0.02, that threshold cannot be exceeded when RMS(φ) is at most 75 g s−1. Table 12 reports all seven feedback conditions from the exploratory re-run. During a brief +15% fault, the four-stage supervisor (C3) reduced adaptation RMSE by 1.273 g s−1 relative to validity- only adaptation (C2) (C3−C2 CI −1.292 to −1.257; Holm-adjusted p = 0.0103). It rejected all 60 first candidates and recorded zero false updates among 180 accepted updates, compared with 60 among 240 for C2. During aligned recurring faults, C3 rejected every candidate, kept the initial scale and reduced RMSE by 3.177 g s−1 (CI −3.239 to −3.115; adjusted p = 0.0103). Rejecting every candidate avoided harmful updates at the cost of leaving the actual plant shift uncorrected. IJEMT Table 12. Exploratory re-run: mean RMSE (g s−1) and false/accepted updates. Feedback condition C2 RMSE C3 RMSE C5 RMSE C2 false / accepted C3 false / accepted Healthy feedback 5.664 5.686 3.093 0 / 239 0 / 225 Brief +15% 8.023 6.750 5.874 60 / 240 0 / 180 Brief −15% 5.664 5.686 3.067 0 / 239 0 / 225 Recurring aligned +15% 11.686 8.509 10.951 173 / 240 0 / 0 (n/e) Recurring random +15% 10.049 8.516 9.813 85 / 235 0 / 1 Persistent +15% 11.941 11.937 14.273 181 / 240 181 / 238 Persistent −15% 5.613 5.613 7.955 0 / 240 0 / 240 Means use 12 independent runs after averaging five network seeds, and event counts cover 60 run–seed pairs. n/e means the false-update rate cannot be estimated because no update was accepted (0/0). A rate calculated from a single accepted update (0/1) provides little evidence about reliability. C1 and C2 were identical because all samples passed the health mask. C5 has no comparable discrete false-update label. The C0–C5 holdout results, full event counts and 21 paired tests are available in the GitHub repository. With random-phase recurring faults, C3 accepted only one update across 60 pairs. Its RMSE difference from C2 was −1.533 g s−1 (CI −2.408 to −0.486), but this was not significant after Holm correction (p = 0.082). Performance varied with the randomly selected fault phase. Under a persistent +15% bias, C3 and C2 recorded 181 false updates each, among 238 and 240 accepted updates, respectively. Their RMSE values were nearly identical (11.937 and 11.941 g s−1). C3 had lower RMSE than RLS for aligned recurring faults and persistent biases, and also for random-phase recurring faults (adjusted p = 0.043). RLS had lower RMSE with healthy feedback and with both brief faults (each adjusted p = 0.0103). With healthy feedback, C3 was slightly worse than C2 (+0.021 g s−1; adjusted p = 0.043). None of the deployable policies achieved the lowest error under every feedback condition. The exploratory results do not change the original FAIL outcome in Table 11. 5. Conclusion Considering speed density, the nominal MAE was decreased 69.9% and transient MAE 64.2% by the residual airflow estimator in simulation. This benefit could only be encouraged within the range of supported operation, had no effect in boundary and corner circumstances, and operated in opposition in high volumetric efficiency mismatch. The four-stage supervisor had only a marginal advantage over simpler policies for post-shift NRMSE, reducing it by 48.2%, and it could not meet the predeclared false-update criterion. Later-window acceptance minimized negative lambda checks for a short time or 'aligned' recurring positive faults, while persistent bias defeated the check. The excitation gate has been found to reject all tested steady-ids windows and the RLS could get lower adaptation error for healthy feedback. It is important to understand that these results are not just an overall calibration improvement, but conditionality. It has been decided that the study will be limited to simulation. For the implementation, it is necessary to measure the parameters of the engine; carry out extensive general fault testing; securely detect lambda drift and the error of the injector flow; embed engine parameters into the IJEMT timing parameter; and validate the ECU interface that is proposed. Results validate and support further experimental testing, but do not provide any means of determining safety or compatibility with the original ECU. Data and code availability. The source code, simulation configurations, trained models, result files and supporting analyses are available at https://github.com/alaa198011/m30-virtual-maf- lambda-calibration. 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