{"id":"6501c68c-0c23-41da-b7d1-994ab615ed26","arxiv_id":"1908.02934","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The authors propagate measurement and probe-position uncertainty through a harmonic least-squares model and propose two variance-like metrics for spatial sampling and measurement imprecision, arguing the standard sampling metric is inadequate.","lead":"This paper extends a Fourier-based method for reconstructing gas turbine temperature fields to include measurement uncertainty, and proposes two new metrics for sampling and measurement imprecision. It argues that standard engine-test sampling uncertainty is misleading, and that measurement error matters more than probe misplacement.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proposed uncertainty metrics are internally inconsistent: Eq. (25) redefines eps_p^2 relative to Eq. (18), and eps_m^2 = mu(eps_p^2) - eps_p^2 is not a well-defined variance, can be negative, and Eq. (27)'s stated limit fails because of the NM vs NM-1 mismatch.","rationale":"The reader's weakest_assumption focused on the Gaussian, homoskedastic, correctly-specified case and model bias contaminating the sampling-error interpretation. My stress-test found a more basic, definitional problem: the paper changes the definition of eps_p^2 between Eq. (18) and Eq. (25), then derives the measurement-imprecision metric eps_m^2 from the mismatch. This is not a disagreement with external consensus; it is an internal consistency issue. The chi-square derivation in Eqs. (19)-(21) is a valid calculation for the random quantity in Eq. (18), but Eq. (25) is a different, deterministic residual, so the 'two new uncertainty metrics' are not rigorously defined as claimed. The reader did flag inconsistent definitions, a dimensionally inconsistent variance formula, and the non-variance nature of eps_m^2 in the rationale, so I partially agree; however, the reader's weakest_assumption emphasized model misspecification, which I see as secondary to the definitional problems. The paper's core least-squares propagation framework may survive revision with consistent definitions, so a conditional accept remains appropriate. The proposed test would settle whether eps_m^2 can be negative and whether Eq. (21)'s variance is indeed missing a factor, thereby confirming that the metrics require correction before adoption.","tokens_in":13369,"tokens_out":7107,"duration_ms":63774,"concrete_test":"Recompute the Engine A entries in Table 2. First, evaluate eps_p^2 by both Eq. (18) (with B as the recorded measurement and X = PB) and Eq. (25) (with mu_B) using the harmonic pair omega = (1,4); then set g = rank(I-H) and phi = ||(I-H)mu_B||^2/sigma_b^2 and compute eps_m^2 = sigma_b^2/(NM)(g+phi) - eps_p^2 from Eq. (25). If for either sigma_b = 0.51 K or 1.02 K the resulting eps_m^2 is negative, the measurement-imprecision metric is not a variance. Also check that sigma^2(eps_p^2) in Eq. (21) matches sigma_b^4/(NM)^2 (2g + 4phi); a mismatch by a factor sigma_b^2/(NM) confirms the dimensional error.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that the two metrics are 'rigorously derived' fails at the definitional level. Eq. (18) defines eps_p^2 = (1/NM)||AX - B||_2^2 as a random variable whose moments are then derived in Eqs. (19)-(21) under B ~ N(mu_B, sigma_b^2 I). Eq. (25) redefines the same symbol as eps_p^2 = (1/(NM-1))||AX - mu_B||_2^2, a deterministic residual against the mean data with denominator NM-1. These are different objects. The measurement imprecision metric Eq. (26), eps_m^2 = mu(eps_p^2) - eps_p^2, then mixes the expectation of the random quantity with the deterministic residual. If eps_p^2 is the random variable, E[eps_m^2] = 0, so it is not an uncertainty. If eps_p^2 is the Eq. (25) deterministic residual, then E[eps_m^2] = (sigma_b^2/(NM))g - ||(I-H)mu_B||^2/(NM(NM-1)), which is not guaranteed to be nonnegative; a claimed variance that can be negative is invalid. Eq. (27) claims limit_{sigma_b -> 0} mu(eps_p^2) = eps_p^2, but substituting Eq. (21) and Eq. (25) gives limit difference = -||(I-H)mu_B||^2/(NM(NM-1)), which is zero only if the model already interpolates the mean data. Independently, the variance formula in Eq. (21) is dimensionally inconsistent: sigma^2(eps_p^2) has units K^2 on the RHS while eps_p^2 has units K^2, so a variance of eps_p^2 should have units K^4; the correct expression is sigma_b^4/(NM)^2 (2g + 4phi). Table 2 reports values that appear incompatible with this. These errors strike at the paper's proposed metrics, not merely the exposition.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a frequentist uncertainty propagation framework for the multivariate linear least-squares temperature-field model introduced in Part I. Measurements are treated as Gaussian with known mean and covariance, probe positions may also be uncertain, and the paper derives moments for the squared residual and for area-averaged predictions. On this basis it proposes two new metrics: a 'spatial sampling uncertainty' epsilon_p^2 and a 'measurement imprecision uncertainty' epsilon_m^2. The numerical sections apply the framework to engine extracts, compare correlated and uncorrelated measurement noise, propagate rake-position uncertainty by Monte Carlo, and argue that the standard AGARD/PTC sampling-uncertainty formula overstates the uncertainty for harmonic flow fields. The paper concludes that measurement imprecision, rather than probe placement, dominates the uncertainty in the reconstructed field.","tokens_in":13797,"tokens_out":8812,"duration_ms":92096,"significance":"The paper addresses a practically important problem: how to decide whether a few rakes suffice to characterize a circumferentially non-uniform temperature field. It gives several useful pieces: the explicit propagation of Gaussian measurement covariance through the pseudoinverse, formulas for the variance of area-averaged temperature, a clear demonstration that the standard sampling-uncertainty formula (1) is misleading for harmonic fields, and a Monte Carlo scheme for probe-position uncertainty. If the proposed metrics were valid, they would be a useful addition to turbomachinery test practice. However, the central metric definitions are internally inconsistent: epsilon_p^2 is defined differently in Eq. (18) and Eq. (25), the variance formula in Eq. (21) is dimensionally wrong, and epsilon_m^2 in Eq. (26) is not a well-defined variance. These are not presentation issues; they invalidate the two headline contributions as stated.","major_comments":[{"comment":"The symbol epsilon_p^2 is defined twice with different meanings. Equation (18) defines epsilon_p^2 = (1/NM)||AX-B||_2^2 with B a Gaussian random matrix, so epsilon_p^2 is a random variable whose moments are then derived in Eqs. (19)-(21). Equation (25) defines epsilon_p^2 = (1/(NM-1))||AX-mu_B||_2^2, a deterministic quantity computed from the mean data, with a different denominator and with B replaced by mu_B. Both objects are called the spatial sampling uncertainty and both are used in Eqs. (26)-(27). The moment formulas of Sec. 4.1 apply to the Eq. (18) object, while the metric used in Table 2 and Algorithm 1 is the Eq. (25) object. The paper never reconciles these two definitions, so the claim that the sampling-uncertainty metric is rigorously derived is not supported.","section":"Sec. 4.3, Eqs. (18) and (25)"},{"comment":"The measurement imprecision metric epsilon_m^2 = mu(epsilon_p^2) - epsilon_p^2 is not a valid variance. If epsilon_p^2 is the random variable of Eq. (18), then E[epsilon_m^2] = 0 and the quantity carries no information about uncertainty. If epsilon_p^2 is instead the deterministic residual of Eq. (25), then epsilon_m^2 is a difference between an expectation and a realized residual, and it is not guaranteed to be nonnegative. A quantity proposed as a variance that can be negative is inadmissible, and the paper provides no other statistical interpretation for epsilon_m^2.","section":"Sec. 4.3, Eq. (26)"},{"comment":"Equation (21) is dimensionally inconsistent. The quantity epsilon_p^2 is a squared temperature residual and therefore has units K^2; its variance sigma^2(epsilon_p^2) must have units K^4. The right-hand side as printed, (sigma_b^2/(NM))(2g+4phi), has units K^2 because sigma_b^2 has units K^2 and g, phi, and NM are dimensionless. The correct expression for the variance of (1/NM)||AX-B||^2 under B ~ N(mu_B, sigma_b^2 I) is sigma_b^4/(NM)^2(2g+4phi). Consequently the values in Table 2, described as sigma^2(epsilon_p^2), cannot be the values obtained from Eq. (21) as written, and the numerical results in Sec. 5 do not validate the printed formula.","section":"Sec. 4.1, Eq. (21)"},{"comment":"The limit in Eq. (27) does not follow from the preceding definitions. Under Eq. (21), lim_{sigma_b->0} mu(epsilon_p^2) = ||(I-H)mu_B||^2/(NM), where H = AP is the hat matrix. Under Eq. (25), epsilon_p^2 = ||AX-mu_B||^2/(NM-1) = ||(I-H)mu_B||^2/(NM-1). The difference is -||(I-H)mu_B||^2/[NM(NM-1)], which is zero only if the harmonic model interpolates the mean data. Thus the stated claim that epsilon_m^2 vanishes as sigma_b -> 0 is generally false.","section":"Sec. 4.3, Eq. (27)"},{"comment":"The reported accuracy of the selected harmonic pairs is partly a selection artifact. Algorithm 1 searches over harmonic pairs and returns those that minimize mu(epsilon_p^2) evaluated on the same data used to fit the model, and Eq. (25) defines epsilon_p^2 as the in-sample least-squares residual. In-sample residuals are biased downward as estimates of out-of-sample error, and Sec. 5.1 explicitly states that no distinction is made between testing and training data. In addition, when the Fourier model is misspecified, the residual ||AX-mu_B||^2 contains model bias as well as sampling variation, so the proposed 'spatial sampling uncertainty' is not a pure sampling uncertainty. The paper does not discuss either of these limitations when presenting the metric in Sec. 4.3.","section":"Sec. 5.2 and Algorithm 1"}],"minor_comments":[{"comment":"The variance expansion in Eq. (6) appears to contain a factor error: the printed expression '= 2 sum_i sum_j ... cov' gives twice the correct total variance and mixes the variance and covariance terms incorrectly; the standard form is sum_i (partial eta/partial z_i)^2 sigma_i^2 + 2 sum_{i= beta, but beta is never defined, and lambda is set to a vector on line 4 while line 9 references lambda_i without making the loop index explicit. This makes the regularization procedure difficult to reproduce.","section":"Algorithms 1 and 2"},{"comment":"The text refers to 'Pearson rank correlation', but Pearson correlation is not a rank correlation; the authors should use either 'Pearson correlation' or 'Spearman rank correlation' consistently.","section":"Fig. 3 caption and Sec. 2.3"},{"comment":"The symbol K denotes the number of probes in Eq. (1) and then the total number of measurements NM = 42 in Eq. (30). Reusing K for different quantities in the same uncertainty discussion is confusing and should be fixed.","section":"Eqs. (1) and (30)"}],"recommendation":"reject","confidential_remarks":"The paper is a Part II companion to an ASME submission, and its central contribution is the pair of uncertainty metrics in Sec. 4.3. The definitional inconsistency between Eq. (18) and Eq. (25), the dimensional error in Eq. (21), and the invalid variance interpretation of Eq. (26) are load-bearing problems that would require re-deriving the core of the paper rather than local edits. I therefore recommend rejection, despite the useful engineering motivation and the correct standard linear algebra in Secs. 4.1-4.2. I would not invite a revision unless the authors are prepared to redefine the metrics and rerun the numerical study."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nYou should know two things about this paper. The motivating observation is genuinely good: the standard sampling-uncertainty metric, a plain standard deviation of rake readings, gives nonzero values even when the spatial pattern is exactly captured, because it ignores the non-uniform field. That is a real problem for engine test engineers. The second thing is less good: the two new metrics the authors offer to fix it are not rigorously derived as claimed. Epsilon_p^2 is defined in Eq. (18) as a random variable, the normalized residual of the noisy data, and then redefined in Eq. (25) as a deterministic residual against the mean data, with a different denominator, NM-1 instead of NM. The measurement-imprecision metric epsilon_m^2 = mu(epsilon_p^2) - epsilon_p^2 then mixes the expectation of the random quantity with the deterministic residual. If epsilon_p^2 is the random variable, the expectation of epsilon_m^2 is zero. If it is the deterministic residual, epsilon_m^2 can be negative. Either way it is not a variance. The limit in Eq. (27) fails for the same reason. The variance formula in Eq. (21) is also dimensionally wrong: the variance of a K^2 quantity should be K^4, but the formula gives K^2. These are not typos; they sit at the center of the paper's contribution.\n\nWhat the paper does well: the propagation of Gaussian measurement noise and probe-position uncertainty through the least-squares harmonic model is standard linear model theory, and the linear algebra in Eqs. (12)-(13) is correct. The numerical sections show clearly that measurement uncertainty dominates probe-position uncertainty for their test cases, and the discussion of ISO/ASME uncertainty frameworks is sensible. The authors also honestly note when the analytical formulas do not apply and Monte Carlo must be used.\n\nThe soft spots beyond the metric definitions: the harmonic pair is selected by brute-force minimizing the same metric on the same data (Algorithm 1 and Sec. 5.1), so the low reported errors are partly in-sample optimism. The comparison in Sec. 6 with the standard metric is apples-to-oranges: the two quantities are not measuring the same thing, so the fact that the standard metric gives larger numbers is expected and not a meaningful critique.\n\nWho is this for: turbomachinery test engineers and anyone using sparse spatial measurements to estimate engine performance. The paper is worth refereeing because the problem is important and the flaws are fixable, but in the current form the proposed metrics should not be adopted as stated.\n\nMy recommendation: send it to peer review, but require the referees to force a consistent definition of epsilon_p^2, a nonnegative quantity that is actually a variance, and validation that separates in-sample fit from predictive sampling uncertainty.","headline":"The motivating observation is solid and the Gaussian propagation is textbook, but the two new uncertainty metrics are not consistently defined and the paper's core claim about rigorous derivation does not hold in its current form.","tokens_in":14370,"tokens_out":5178,"would_cite":false,"duration_ms":48777,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the standard sampling-uncertainty metric overstates engine temperature uncertainty by a factor of about three, and proposes two propagation-based metrics—spatial sampling uncertainty and measurement imprecision—to…","keywords":["uncertainty quantification","spatial sampling uncertainty","measurement imprecision","harmonic least squares","temperature rake measurements","non-central chi-square distribution","uncertainty propagation"],"falsifier":"On a real engine extract with a known temperature field containing harmonics beyond the chosen pair, compute $\\epsilon_p^2$ from equation (25) while also measuring the true reconstruction error against a dense traverse; if $\\epsilon_p^2$ stays near zero while the reconstruction error is large, the metric is not actually capturing sampling deficiency.","tokens_in":13112,"feed_emoji":"🌡️","tokens_out":6026,"duration_ms":63685,"temperature":0.7,"pith_summary":"This paper extends a harmonic least-squares model of engine temperature fields—built in the companion Part I—into a full uncertainty-propagation framework. Its central claim is that the customary sampling-uncertainty metric, the standard deviation of a few rake measurements, overstates engine temperature uncertainty and can mislead engineers about whether more rakes are needed. The paper derives two replacement metrics: one for spatial sampling uncertainty and one for measurement imprecision, and shows analytically, under uncorrelated Gaussian measurement noise, that the model's error follows a non-central chi-square distribution. Numerically, the paper reports that uncertainty in individual temperature measurements and their correlations matters far more than uncertainty in rake positions, and that the standard metric gives bounds roughly three times larger than the proposed framework. If correct, testers could use the proposed metrics to decide whether a few rakes suffice and to separate instrument error from spatial coverage error.","feed_headline":"Two new metrics replace the old rake-sampling uncertainty","feed_subtitle":"Measurement error, not probe position, drives engine temperature uncertainty—and the old metric overstates it by ~3x.","key_machinery":"The central object is the multivariate harmonic least-squares model $T(r,\\theta) = v^T(r) U X^T a(\\theta)$, with Fourier matrix $A$ encoding the chosen harmonic pair; uncertainty is propagated by treating the measurements as $B \\sim \\mathcal{N}(\\mu_B, \\Sigma_B)$ and pushing the covariance through the pseudoinverse $P = (A^T A)^{-1} A^T$ into coefficient covariance $\\Sigma_X = (I_M \\otimes P)\\Sigma_B (I_M \\otimes P)^T$ and field covariance $\\Sigma_F$. The load-bearing identity is that, when $\\Sigma_B = \\sigma_b^2 I$, the quantity $NM\\,\\epsilon_p^2/\\sigma_b^2$ follows a non-central chi-square distribution with degrees of freedom $g = \\text{rank}(\\Sigma_R)$ and non-centrality parameter $\\phi = \\text{vec}(\\mu_R)^T \\Sigma_R^- \\text{vec}(\\mu_R)$; equations (19)–(21) give the mean and variance. This identity converts the vague notion of “sampling uncertainty” into a computable variance, and yields the two proposed metrics: $\\epsilon_p^2$ for sampling and $\\epsilon_m^2 = \\mu(\\epsilon_p^2) - \\epsilon_p^2$ for measurement imprecision.","core_discovery":"On the paper's own terms, the discovery is that sampling uncertainty cannot be defined without a spatial model: the same perfectly captured single-harmonic pattern yields standard-deviation sampling uncertainties of 0.64 K, 0.91 K, and nonzero even with 300 rakes, so the conventional metric tracks the non-uniformity of the field rather than the adequacy of the sample. The paper therefore defines spatial sampling uncertainty as $\\epsilon_p^2 = \\frac{1}{NM-1}\\|AX-\\mu_B\\|_2^2$, the squared norm of the residual between the harmonic model evaluated at the chosen coefficients and the measured mean, and measurement imprecision uncertainty as the difference between the total expected squared error and that sampling term. It then proves that under Gaussian uncorrelated noise the total error is a non-central chi-square variable, so both the mean and variance of $\\epsilon_p^2$ have closed forms. Numerical experiments on engine extracts show that temperature measurement uncertainty dominates rake-position uncertainty, and that correlated measurement chains reduce spatial temperature uncertainty compared with uncorrelated ones; the standard root-sum-square sampling uncertainty is about three times larger than the proposed framework's bound.","pith_inferences":["If the harmonic model is misspecified—the real field contains harmonics not in $A$—then $\\epsilon_p^2$ will absorb the resulting bias, so the “sampling uncertainty” label conflates sampling error with model error; a separate model-bias diagnostic would be needed.","The same quadratic-form machinery could be applied with a whitening transformation to handle correlated Gaussian noise analytically, rather than falling back to Monte Carlo, at the cost of introducing the inverse covariance matrix into the chi-square parameters.","The finding that positive correlations reduce spatial temperature uncertainty mirrors the efficiency-level result the paper reproduces from its reference [16], suggesting a general principle: common-mode calibration error moves uncertainty from the spatial pattern to the overall level, which matters for absolute temperature but not for pattern shape.","A natural testable extension is to compute $\\epsilon_p^2$ and $\\epsilon_m^2$ on a rig where a dense traverse gives the truth, and compare the proposed sampling metric against actual reconstruction error—this would validate whether the metric can serve as a stopping rule for rake count."],"forward_implications":["For a fixed harmonic pair and uncorrelated Gaussian probe noise, an engineer can compute the mean and variance of the spatial reconstruction error in closed form, without Monte Carlo.","The proposed $\\epsilon_p^2$ will be large when the harmonic frequencies are poorly chosen or too few, giving a direct, model-based criterion for adding rakes or harmonics.","Because measurement uncertainty dominates probe-position uncertainty, effort spent improving probe calibration and characterizing correlations should reduce spatial temperature uncertainty more than tightening rake positioning.","Correlated temperature measurement chains shrink the spatial uncertainty compared with independent probes, so calibration strategy becomes part of the uncertainty budget.","The conventional standard-deviation sampling uncertainty should not be used as a standalone bound; the paper shows it can overstate uncertainty by roughly a factor of three on a four-harmonic synthetic temperature profile."],"supporting_citations":[{"why":"Supplies the harmonic least-squares model and area-average formulas that this paper propagates uncertainty through.","marker":"[1]"},{"why":"Provides the theorem on non-central chi-square distributions of quadratic forms that underlies equations (19)–(21).","marker":"[22]"},{"why":"Introduces the standard sampling-uncertainty definition that the paper argues against and seeks to replace.","marker":"[10]"},{"why":"Defines the decomposition of temperature uncertainties into calibration, data-acquisition, and sampling components that motivates the measurement-imprecision metric.","marker":"[11]"},{"why":"Sets out the type A/type B uncertainty taxonomy and the law of propagation of uncertainty that frame the paper's approach.","marker":"[2]"},{"why":"Reports that positive correlations among measured temperatures reduce efficiency uncertainty, a result the paper reproduces and extends to spatial temperature fields.","marker":"[16]"},{"why":"Provides the Coleman–Steele uncertainty-analysis workflow used for the first-order Taylor series propagation in Section 2.","marker":"[12]"}],"fun_headline_variants":["New metrics replace old rake-sampling uncertainty","Measurement error, not probe position, drives uncertainty","Old sampling metric overstates uncertainty by 3x","Two new metrics redefine spatial sampling uncertainty","Why the old sampling metric fails: new framework"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the measurement noise is Gaussian with equal variance across probes and no correlations, and that the chosen harmonic pair is the true model that generated the data; if either fails, the analytical chi-square expressions and the clean interpretation of $\\epsilon_p^2$ as pure sampling uncertainty no longer hold.","fun_headline_variants_meta":{"raw":{"variants":["New metrics replace old rake-sampling uncertainty","Measurement error, not probe position, drives uncertainty","Old sampling metric overstates uncertainty by 3x","Two new metrics redefine spatial sampling uncertainty","Why the old sampling metric fails: new framework"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1469,"prompt_tokens":984,"completion_tokens":485,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":416}},"tokens_in":600,"tokens_out":485,"duration_ms":5732,"temperature":1.0,"reasoning_tokens":416,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:29:25.059335+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a real engine extract with a known temperature field containing harmonics beyond the chosen pair, compute $\\epsilon_p^2$ from equation (25) while also measuring the true reconstruction error against a dense traverse; if $\\epsilon_p^2$ stays near zero while the reconstruction error is large, the metric is not actually capturing sampling deficiency.","supporting_citations":[{"cited_title":"Spatialflow-fieldap- proximationusingfewthermodynamicmeasurementsPartI:formulationandareaaveraging","cited_arxiv_id":null,"evidence_quote":"Supplies the harmonic least-squares model and area-average formulas that this paper propagates uncertainty through."},{"cited_title":"Generalized inverse of a matrix and its applications","cited_arxiv_id":null,"evidence_quote":"Provides the theorem on non-central chi-square distributions of quadratic forms that underlies equations (19)–(21)."},{"cited_title":"Suitable Averaging Techniques in Non-Uniform Internal Flows","cited_arxiv_id":null,"evidence_quote":"Introduces the standard sampling-uncertainty definition that the paper argues against and seeks to replace."},{"cited_title":"Recommended Practices for Measurement of Gas Path Pressures andTemperaturesforPerformanceAssessmentofAircraftTurbineEnginesandComponents","cited_arxiv_id":null,"evidence_quote":"Defines the decomposition of temperature uncertainties into calibration, data-acquisition, and sampling components that motivates the measurement-imprecision metric."},{"cited_title":"InternationalOrganization for Standardization, Geneva","cited_arxiv_id":null,"evidence_quote":"Sets out the type A/type B uncertainty taxonomy and the law of propagation of uncertainty that frame the paper's approach."},{"cited_title":"Temperature measurement system for low pressure ratio turbine testing","cited_arxiv_id":null,"evidence_quote":"Reports that positive correlations among measured temperatures reduce efficiency uncertainty, a result the paper reproduces and extends to spatial temperature fields."},{"cited_title":"Engineering application of experimental uncer- tainty analysis","cited_arxiv_id":null,"evidence_quote":"Provides the Coleman–Steele uncertainty-analysis workflow used for the first-order Taylor series propagation in Section 2."}],"review_version":1}