Multivariate Time Series Analysis of Temperatures in the Archaeological Museum of L’Almoina (Valencia, Spain)
<p>Plan of the L’Almoina archaeological site, indicating the position of 27 data-loggers for monitoring the air conditions inside the museum. Based on the multivariate analysis of temperatures (see <a href="#sec3dot3dot6-sensors-21-04377" class="html-sec">Section 3.3.6</a>), three zones were established: North West (NW, in blue), South East (SE, in green) and Skylight (Sk, in orange). The different observable structures and the construction phases in the museum are indicated: (a) Roman baths; (b) Imperial granary; (c) Portico of the imperial forum; (d) Imperial chapel; (e) Imperial basilica; (f) Byzantine apse and tombs; (g) Byzantine Cathedral Baptistery; (h) Republican and Imperial Asklepieion; (i) Alcázar Aldalusí; (j) Decumani; and (k) Cardus [<a href="#B12-sensors-21-04377" class="html-bibr">12</a>].</p> "> Figure 2
<p>View of the skylight covering part of L’Almoina archaeological site: (<b>a</b>) external view from the pedestrian plaza; and (<b>b</b>) internal view.</p> "> Figure 3
<p>Trajectories of the different time series of T from the 27 sensors located in the museum. Values were recorded between 22 October 2019 and 20 October 2020. The separation of different stages (Wr1, Cd, Tr, Ht and Wr2) is indicated by means of solid vertical lines. Dashed vertical lines indicate the structural breaks identified within the stages Wr1, Cd and Ht.</p> "> Figure 4
<p>Summary of steps involved in method M1: blue lines, Type 1 classification variables; green lines, Type 2 variables; solid lines, process; dashed line, results. Different boxes contain the name of the stages (i.e., Wr1A, Wr1B, CdA, CdB, Tr, HtA, HtB and Wr2) to indicate that the procedure was applied to all parts of the time series. A structural break was found in Wr1, Cd and Ht, so that the suffixes A and B denote the substages before and after the break, respectively.</p> "> Figure 5
<p>Summary of steps in method M2: blue lines, Type 3 classification variables; green lines, Type 4 variables; red lines, Type 5 variables; solid lines, process; dashed line, results.</p> "> Figure 6
<p>Summary of steps in method M3: blue lines, Type 6 classification variables; green lines, Type 7 variables; solid lines, process; dashed line, results.</p> "> Figure 7
<p>Summary of steps of method M4: red lines, Type 7 variables of M3; green lines, Type 8 variables; solid lines, process; dashed line, results.</p> "> Figure 8
<p>Results associated with the k-means method. (<b>a</b>) Absolute frequency (number) of indices that indicates the best number of classes in the museum. For example, two classes are selected by seven indices. (<b>b</b>) Classification of sensors installed in the museum, according to the k-means method. Each color (blue, green and orange) corresponds to a different class.</p> "> Figure 9
<p>Evaluation of the PLS-DA performance for the classification of sensors into three categories. Vertical axes indicate the classification error rate (CER) for each prediction distance as a function of the number of components (horizontal axis) for: M1 (<b>a</b>); M2 (<b>b</b>); M3 (<b>c</b>); M4 (<b>d</b>); and using the variables from all methods (<b>e</b>). Three types of prediction distances were considered: Mahalanobis (green lines), maximum (blue lines) and centroid (red lines). Two types of CER were computed: balanced error rate (dashed lines) and overall error rate (solid lines). PLS-DA was carried out using repeated three-fold CV 1000 times.</p> "> Figure 10
<p>Evaluation of the PLS-DA performance (considering three components) for the classification of sensors into three categories. Vertical axes indicate the Balance error rate (BER) per component (orange lines, Component 1; green lines, Component 2; and blue lines, Component 3). BER values were computed across all folds using 5, 10 or 15 variable (horizontal axes) for eachmethod: M1 (<b>a</b>);M2 (<b>b</b>);M3 (<b>c</b>);M4 (<b>d</b>); and all methods (Ms) (<b>e</b>). The three-fold CV technique was run 1000 times, using maximum distance prediction. Diamonds highlight the optimal number of variables per component.</p> "> Figure 11
<p>Error rates derived from the sPLS-DA and RF algorithms. Red points are OOB classification error rates per method, based on different sets of classification variables: M1, M2, M3, M4 and all variables (Ms). Blue points are mean values of BER for all the components, per method, for sPLS-DA.</p> "> Figure 12
<p>Projection of sensors over the three relevant components (C1–C3) from sPLS-DA, per method (M1–M4) or when using all variables (Ms). Graphs show discrimination of the sensors, according to three classes: North Western (NW), South Eastern (SE) and Skylight (Sk). Color codes: NW sensors in blue, Sk in orange and SE in green. Each graph displays a confidence ellipse for each class (at a confidence level of 95%), in order to highlight the strength of the discrimination.</p> "> Figure 12 Cont.
<p>Projection of sensors over the three relevant components (C1–C3) from sPLS-DA, per method (M1–M4) or when using all variables (Ms). Graphs show discrimination of the sensors, according to three classes: North Western (NW), South Eastern (SE) and Skylight (Sk). Color codes: NW sensors in blue, Sk in orange and SE in green. Each graph displays a confidence ellipse for each class (at a confidence level of 95%), in order to highlight the strength of the discrimination.</p> "> Figure 13
<p>(<b>a</b>) Projection of sensors over components C1 and C2 from sPLS-DA for M1. The graph displays a good discrimination of the sensors according to the classes. They are color coded according to the zone where the sensor is located: NWin blue, SE in green and Sk in orange. The most important variables for (<b>b</b>) C1 (<b>c</b>) and C2, according to the absolute value of their coefficients, are ordered from bottom to top. The color corresponds to the zone in which the variable yields the highest mean component value.</p> ">
Abstract
:1. Introduction
2. Background
2.1. Studies for the Long-Term Preservation of Artworks
2.2. European Standards
2.3. Characteristics of the L’Almoina Museum
3. Materials and Methods
3.1. Materials: Description of the Datasets
3.2. Data Calibration
3.3. Statistical Methods
3.3.1. Identification of Structural Breaks in the Time Series
3.3.2. Calculation of Classification Variables—Method M1
3.3.3. Calculation of Classification Variables—Method M2
3.3.4. Calculation of Classification Variables—Method M3
3.3.5. Calculation of Classification Variables—Method M4
3.3.6. Determination of Number of Classes and Class per Sensor Using PCA and K-Means Algorithm
3.3.7. Sensor Classification Using sPLS-DA
3.3.8. Sensor Classification Using Random Forest Algorithm
4. Results and Discussion
4.1. Identification of Structural Breaks in the Time Series
4.2. Calculation of Classification Variables—M1–M4
4.3. Determination of Number of Classes and Class per Sensor Using PCA and K-Means Algorithm
4.4. Sensor Classification Using sPLS-DA
- ☐
- Selected variables from M1: PACF at lags 1–4, MR and parameters of the sample ACF (mean, range, median and mean) (Table 3 (a)).
- ☐
- Selected variables from M2: Level, slope, some seasonal components (5, 8, 10–12, 16–21 and 23), mean and median of sample ACF (residuals), SSE (residuals) and maximum of the periodogram (residuals) (Table 3 (b)).
- ☐
- Selected variables from M3: Parameters of MA, SAR and SMA of seasonal ARIMA models, PACF at lags 1–5 (residuals), mean and median of sample ACF (residuals), statistic of KM normality test (residuals) and frequency for the maximum of the periodogram (residuals) (Table 4 (a)).
- ☐
- Selected variables from M4: The first four Wold coefficients, mean and median of sample ACF (residuals), statistics of the SW and KM normality tests (residuals), PACF at first five lags (residuals), variance (residuals) and maximum of the periodogram (residuals) (see Table 4 (b)).
- ☐
- Selected variables when using the total set of variables from the four methods (some values are highlighted in bold and blue in Table 3 and Table 4): Slope (M2), some seasonal components (2, 3, 5, 8, 11, 12, 14, 16–18 and 21–23) (M2); SSE (M2); Wold Coefficient 1 (M4); mean (M1–M4), median (M2), range (M1 and M2) and variance (M1 and M2) of sample ACF values; and maximum of the periodogram (M2–M4).
C1 | C2 | C3 | ||||
---|---|---|---|---|---|---|
Stage | V | Stage | V | Stage | V | |
(a) For Method 1 | ||||||
1 | Tr | pacf2 | Wr2 | acf.r | CdA | pacf3 |
2 | Tr | acf.m | Wr2 | acf.v | Wr1A | pacf4 |
3 | HtA | pacf2 | HtA | acf.m | CdA | pacf4 |
4 | HtA | pacf1 | CdB | pacf1 | Wr1A | acf.r |
5 | HtB | pacf1 | CdB | M | Wr1A | acf.v |
6 | CdB | pacf2 | Wr1B | M | Wr1A | rMh |
7 | Wr2 | pacf1 | HtB | M | Wr1B | rMh |
8 | Wr1B | pacf1 | Wr1A | M | CdA | rMh |
9 | CdA | pacf1 | CdA | pacf1 | CdB | rMh |
10 | HtB | pacf2 | Wr1B | acf.r | Tr | rMh |
11 | Wr1B | pacf3 | Wr1B | acf.v | HtA | rMh |
12 | Tr | M | Wr2 | pacf2 | HtB | rMh |
13 | HtA | pacf4 | CdA | pacf2 | Wr2 | rMh |
14 | Tr | pacf4 | HtA | acf.r | ||
15 | Wr2 | acf.m | HtA | acf.v | ||
(b) For Method 2 | ||||||
1 | HtA | sse | HtA | acf.m | ||
2 | Tr | sse | HtA | acf.md | ||
3 | Tr | s18 | HtA | s12 | ||
4 | Tr | b | HtA | s11 | ||
5 | Tr | s16 | HtA | acf.r | ||
6 | HtB | sse | CdA | acf.v | ||
7 | Tr | s17 | HtA | acf.v | ||
8 | HtB | s21 | HtA | s23 | ||
9 | Tr | spec.mx | CdA | s14 | ||
10 | Wr2 | s20 | CdA | s5 | ||
11 | HtB | acf.m | Tr | a | ||
12 | Wr1B | s12 | CdA | s10 | ||
13 | Wr2 | acf.md | HtA | s8 | ||
14 | HtB | s19 | HtA | s10 | ||
15 | HtB | s23 | Wr1A | acf.m |
C1 | C2 | C3 | ||||
---|---|---|---|---|---|---|
Stage | V | Stage | V | Stage | V | |
(a) For Method 3 | ||||||
1 | Tr | acf.m | CdA | acf.m | ||
2 | HtA | res.v | CdA | pacf4 | ||
3 | Tr | ma1 | CdA | pacf5 | ||
4 | HtB | ma1 | Wr2 | pacf4 | ||
5 | Tr | kolg.t | Tr | sar2 | ||
6 | CdB | pacf2 | ||||
7 | HtB | pacf1 | ||||
8 | Wr2 | sar2 | ||||
9 | CdA | sar1 | ||||
10 | HtA | sma1 | ||||
11 | HtA | pacf3 | ||||
12 | HtA | freq | ||||
13 | HtA | pacf1 | ||||
14 | HtB | acf.md | ||||
15 | Wr1A | pacf5 | ||||
(b) For Method 4 | ||||||
1 | HtA | psi1 | HtA | pacf5 | Wr1B | psi1 |
2 | HtA | spec.mx | HtB | pacf1 | CdB | acf.m |
3 | HtA | res.v | Wr2 | acf.v | CdB | spec.mx |
4 | Tr | psi1 | HtA | shap.t | Wr2 | acf.m |
5 | Wr1A | acf.m | HtA | acf.m | Wr2 | shap.t |
6 | Wr2 | acf.r | ||||
7 | Tr | pacf1 | ||||
8 | Tr | acf.md | ||||
9 | Wr1B | psi4 | ||||
10 | CdA | pacf5 | ||||
11 | Tr | psi3 | ||||
12 | CdA | acf.md | ||||
13 | Wr2 | psi2 | ||||
14 | Tr | kolg.t | ||||
15 | Wr2 | kolg.t |
4.5. Sensor Classification Using Random Forest Algorithm
- ☐
- Selected variables from M1: Mean, range and variance of the sample ACF values, the first four values of sample PACF, the maximum value of the periodogram and the mean.
- ☐
- Selected variables from M2: Level, slope and 18 seasonal components (2, 3, 7–12, 14 and 16–24) from sH-W method, SSE, maximum of the periodogram values, statistic of the KS normality test and 17th prediction of T.
- ☐
- Selected variables from M3: First term of the AR, MA and SMA components of the seasonal ARIMA models, sample PACF at lags 1, 2 and 5, mean and median of the sample ACF values, residual variance, maximum of the periodogram values and statistic of the KS normality test.
- ☐
- Selected variables from M4: Coefficients 1, 3, 4 and 5 from the Wold decomposition; the first five values of the sample PACF; the mean, median, range and variance of the sample ACF values; residual variance; maximum of the periodogram values of the residuals; and statistics of both the SH and KS normality tests.
- ☐
- Selected variables when using all classification variables from the four methods (Ms): mean (M1–M3), median (M2 and M3), range (M2) and variance (M2) of the sample ACF values; sample PACF at lags 1 (M1 and M3), 2 (M1) and 3 (M1); first coefficient of the Wold decomposition (M3); and statistic of the KS normality test (M2) (the results from Ms comprise 20% of variables from M1, 60% from M2, 9% from M3 and 11% from M4).
M1 | M2 | M3 | M4 | Ms | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Stage | V | Stage | V | Stage | V | Stage | V | M | Stage | V | |
1 | CdA | pacf1 | HtA | sse | Tr | acf.m | HtA | psi1 | M1 | CdA | pacf1 |
2 | HtA | pacf4 | HtA | s24 | HtA | sma1 | CdB | psi1 | M2 | HtA | sse |
3 | HtA | pacf1 | HtA | s23 | Tr | acf.md | Tr | res.v | M3 | Tr | acf.m |
4 | Tr | pacf2 | HtA | s8 | CdB | pacf2 | HtA | pacf5 | M2 | HtA | s24 |
5 | CdB | pacf2 | HtA | s11 | HtA | res.v | HtA | res.v | M4 | HtA | psi1 |
6 | HtA | acf.m | HtA | s12 | Tr | kolg.t | Tr | acf.m | M1 | HtA | pacf4 |
7 | Tr | acf.m | HtB | acf.m | HtA | spec.mx | Tr | spec.mx | M2 | HtA | s23 |
8 | CdA | acf.m | CdA | acf.v | CdB | ma1 | Tr | psi1 | M3 | HtA | sma1 |
9 | Tr | pacf1 | Tr | sse | Tr | ma1 | Tr | kolg.t | M2 | HtA | s8 |
10 | HtB | pacf2 | HtA | acf.r | HtA | pacf1 | CdA | pacf1 | M2 | HtA | s11 |
11 | HtB | M | HtA | acf.md | CdA | pacf5 | HtA | spec.mx | M2 | HtA | acf.r |
12 | Wr2 | acf.m | Wr2 | s23 | HtA | ar1 | Wr1A | acf.m | M2 | HtA | s12 |
13 | Wr2 | pacf1 | Wr1B | a | Wr1A | sar2 | CdA | acf.md | M2 | HtA | acf.m |
14 | CdB | pacf1 | Tr | b | Wr1A | acf.md | CdA | pacf4 | M2 | CdA | acf.v |
15 | Tr | M | HtA | s22 | Tr | spec.mx | CdA | acf.v | M2 | Wr1B | a |
16 | Wr2 | acf.v | Tr | s16 | CdA | acf.m | HtB | res.v | M2 | HtA | s22 |
17 | Wr2 | pacf2 | Tr | a | Tr | res.v | CdA | kolg.t | M2 | HtB | acf.m |
18 | HtA | pacf2 | Tr | s17 | HtB | ma1 | Wr1A | psi1 | M1 | HtA | pacf1 |
19 | Wr2 | acf.r | CdA | s10 | HtB | sar2 | Wr1B | acf.m | M2 | HtA | acf.md |
20 | CdA | M | CdA | a | HtB | pacf1 | Tr | pacf1 | M3 | Tr | acf.md |
21 | Wr1B | M | HtA | acf.v | CdB | kolg.t | Tr | pacf5 | M2 | HtA | s9 |
22 | HtB | pacf1 | Wr2 | s18 | CdA | sar1 | HtB | psi1 | M2 | Wr2 | s23 |
23 | Wr1B | pacf3 | HtB | kolg.t | HtA | pacf3 | Tr | acf.md | M2 | Tr | s17 |
24 | HtA | M | Wr2 | s19 | HtA | pacf5 | Wr2 | pacf4 | M2 | CdA | a |
25 | CdB | M | HtB | s21 | Tr | freq | CdA | acf.m | M1 | Tr | pacf2 |
26 | Wr1A | pacf4 | HtA | s10 | Wr1B | acf.md | HtA | shap.t | M2 | Tr | sse |
27 | HtB | pacf4 | HtB | s9 | Wr1A | ma1 | HtA | acf.m | M2 | HtA | acf.v |
28 | Wr1B | pacf2 | Tr | spec.mx | Wr1B | psi4 | M4 | CdB | psi1 | ||
29 | HtB | spec.mx | Tr | s18 | Wr2 | res.v | M2 | HtA | s10 | ||
30 | Wr1B | acf.m | CdA | s5 | CdA | pacf5 | M2 | Tr | spec.mx | ||
31 | HtA | pacf3 | Tr | s20 | Wr2 | acf.r | M3 | CdB | pacf2 | ||
32 | Wr1B | pacf1 | CdA | s14 | CdA | shap.t | M2 | Tr | s16 | ||
33 | CdA | pacf3 | CdA | s1 | Wr2 | acf.v | M2 | Tr | b | ||
34 | CdB | pacf4 | HtA | acf.m | HtB | pacf1 | M2 | Wr2 | s20 | ||
35 | Wr1A | pacf2 | HtA | s9 | Wr2 | spec.mx | M3 | CdB | ma1 | ||
36 | Wr1A | M | Wr2 | s17 | Wr1B | psi3 | M2 | CdA | s1 | ||
37 | CdA | pacf2 | All | pred.18 | Wr2 | pacf2 | M2 | CdA | s10 | ||
38 | Tr | acf.v | CdA | s22 | Wr1B | pacf5 | |||||
39 | Wr2 | pacf4 | HtA | spec.mx | CdB | shap.t | |||||
40 | Tr | pacf4 | Wr2 | s3 | HtA | psi5 | |||||
41 | HtA | spec.mx | CdA | s23 | Tr | shap.t | |||||
42 | CdB | acf.m | Wr2 | s2 | Wr1A | pacf5 | |||||
43 | Tr | acf.r | Wr2 | kolg.t | |||||||
44 | HtB | acf.m | CdA | pacf3 |
4.6. Methodology to Select a Subset of Sensors for Future Monitoring Experiments in the Museum
- ☐
- For NW, the number of representative sensors was . The 13 sensors in this zone were classified in each of the three concentric circles, as follows: D2, D5, A6 and C6 for the first area (G1); B6, B5, A5 and A4 for the second area (G2); and D6, D3, F, D1 and C5 for the third area (G3). The number of representative sensors selected per group (G1–G3) in this NW class was decided according to the variance of the distances: one sensor in G1, three in G2 and two in G3. The proposed subset of representative sensors is the following: D2 (for G1); B6, A5 and A4 (for G2); and D6 and F (for G3).
- ☐
- For SE, the number of representative sensors was . The eight sensors in this zone were classified according to the concentric circles as: C0 (G1); A and B (G2); and C, C1, B1, D and G (G3). The number of SE sensors selected per group was determined based on the variance of the distances: one sensor in G1, one in G2 and four in G3. The proposed subset of representative sensors is as follows: C0 (for G1); A (for G2); and C, B1, D and G (for G3).
- ☐
- For Sk, the number of representative sensors was established as . The six sensors regarded as Sk were classified as: A2 and A3 (G1); B2, B3 and B4 (G2); and C3 (G3). The number of sensors chosen per group was decided according to the variance of the distances: one in G1, one in G3 and two in G2. The proposed subset of representative sensors was: A3 (for G1); B2 and B4 (for G2); and C3 (for G3).
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Stage | Model | LBQ | LM |
---|---|---|---|
(a) For Method 3 | |||
Wr1A | Seasonal ARIMA | 77.00 | 92.52 |
Wr1B | Seasonal ARIMA | 3.00 | 44.44 |
CdA | Seasonal ARIMA | 25.00 | 77.77 |
CdB | Seasonal ARIMA | 18.00 | 18.52 |
Tr | Seasonal ARIMA | 11.00 | 3.70 |
HtA | Seasonal ARIMA | 22.00 | 22.22 |
HtB | Seasonal ARIMA | 0.00 | 37.04 |
Wr2 | Seasonal ARIMA | 18.00 | 37.04 |
(b) For Method 4 | |||
Wr1A | A seasonal ARIMA per sensor | 92.59 | 96.30 |
Wr1B | A seasonal ARIMA per sensor | 51.85 | 59.26 |
CdA | A seasonal ARIMA per sensor | 81.48 | 81.48 |
CdB | A seasonal ARIMA per sensor | 48.15 | 25.93 |
Tr | A seasonal ARIMA per sensor | 25.93 | 3.70 |
HtA | A seasonal ARIMA per sensor | 59.26 | 29.63 |
HtB | A seasonal ARIMA per sensor | 25.93 | 44.44 |
Wr2 | A seasonal ARIMA per sensor | 55.55 | 37.04 |
Sensors | ||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Stage | Order | D | B | A | C | G | B2 | B3 | B4 | A3 | A2 | C3 | B5 | C5 | C6 | D6 | D5 | A4 | A5 | B6 | A6 | F | D1 | D3 | C0 | C1 | B1 | D2 |
Wr1A | p | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 2 | 2 | 0 |
q | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 3 | 1 | 1 | 1 | 2 | 1 | 3 | 2 | 1 | 0 | 0 | 0 | 2 | 1 | 3 | 0 | 0 | 1 | |
P | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Wr1B | p | 1 | 1 | 1 | 1 | 1 | 0 | 2 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 2 | 1 | 2 | 3 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
q | 1 | 1 | 1 | 1 | 2 | 1 | 0 | 2 | 2 | 2 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | |
P | 2 | 2 | 2 | 2 | 2 | 0 | 2 | 2 | 2 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
CdA | p | 1 | 0 | 0 | 0 | 1 | 2 | 0 | 2 | 1 | 1 | 2 | 2 | 1 | 0 | 0 | 1 | 3 | 0 | 0 | 2 | 3 | 0 | 1 | 0 | 1 | 0 | 1 |
q | 1 | 1 | 2 | 2 | 3 | 0 | 2 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 2 | 0 | 2 | 0 | 3 | 1 | 1 | 0 | 3 | 1 | |
P | 2 | 2 | 2 | 2 | 0 | 2 | 0 | 2 | 2 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 2 | 0 | 2 | 0 | 1 | 2 | 2 | 2 | 2 | |
Q | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 0 | 2 | 0 | 0 | 1 | 0 | 2 | 2 | 1 | 2 | 0 | 1 | |
CdB | p | 0 | 0 | 0 | 0 | 3 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 3 | 3 | 1 | 3 | 1 | 3 |
q | 2 | 1 | 3 | 3 | 0 | 3 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 0 | 1 | 1 | 2 | 3 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | |
P | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
HtA | p | 2 | 1 | 2 | 1 | 3 | 0 | 0 | 3 | 0 | 2 | 3 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 2 | 0 | 3 | 1 |
q | 2 | 3 | 0 | 1 | 1 | 1 | 3 | 0 | 4 | 2 | 0 | 1 | 2 | 1 | 3 | 3 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 2 | 2 | 1 | 1 | |
P | 0 | 0 | 2 | 2 | 0 | 2 | 1 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | 0 | 0 | 2 | 0 | 2 | |
Q | 1 | 1 | 1 | 1 | 1 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | |
HtB | p | 2 | 3 | 0 | 0 | 1 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 0 | 3 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 2 | 0 | 2 | 0 | 0 |
q | 1 | 0 | 2 | 1 | 1 | 2 | 1 | 2 | 0 | 2 | 2 | 1 | 1 | 0 | 3 | 0 | 2 | 2 | 2 | 1 | 0 | 1 | 0 | 3 | 0 | 2 | 1 | |
P | 0 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Tr | p | 2 | 3 | 0 | 0 | 3 | 0 | 1 | 0 | 1 | 0 | 3 | 1 | 3 | 3 | 3 | 3 | 1 | 3 | 0 | 3 | 0 | 3 | 1 | 0 | 3 | 0 | 1 |
q | 0 | 0 | 1 | 3 | 0 | 1 | 3 | 3 | 1 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 3 | 0 | 1 | 3 | 0 | 3 | 2 | |
P | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
Wr2 | p | 3 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 1 | 3 | 2 | 0 | 0 | 2 | 1 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
q | 0 | 1 | 3 | 0 | 2 | 3 | 3 | 1 | 3 | 0 | 2 | 2 | 0 | 1 | 3 | 3 | 0 | 2 | 2 | 0 | 0 | 3 | 2 | 2 | 3 | 3 | 2 | |
P | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Q | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
M1 | M2 | M3 | M4 | Ms | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Stage | C1 | C2 | C3 | C1 | C2 | C1 | C2 | C1 | C2 | C3 | C1 | C2 | C3 |
Wr1A | 0.00 | 6.70 | 30.80 | 0.00 | 6.70 | 0.00 | 6.70 | 20.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Wr1B | 13.30 | 20.00 | 7.70 | 6.70 | 0.00 | 0.00 | 0.00 | 0.00 | 6.70 | 20.00 | 0.00 | 0.00 | 33.30 |
CdA | 6.70 | 13.30 | 23.10 | 0.00 | 26.70 | 0.00 | 26.70 | 0.00 | 13.30 | 0.00 | 0.00 | 20.00 | 6.70 |
CdB | 6.70 | 13.30 | 7.70 | 0.00 | 0.00 | 0.00 | 6.70 | 0.00 | 0.00 | 40.00 | 0.00 | 0.00 | 53.30 |
Tr | 26.70 | 0.00 | 7.70 | 40.00 | 6.70 | 60.00 | 6.70 | 20.00 | 26.70 | 0.00 | 60.00 | 6.70 | 0.00 |
HtA | 20.00 | 20.00 | 7.70 | 6.70 | 60.00 | 20.00 | 26.70 | 60.00 | 20.00 | 0.00 | 20.00 | 60.00 | 6.70 |
HtB | 13.30 | 6.70 | 7.70 | 33.30 | 0.00 | 20.00 | 13.30 | 0.00 | 6.70 | 0.00 | 20.00 | 0.00 | 0.00 |
Wr2 | 13.30 | 20.00 | 7.70 | 13.30 | 0.00 | 0.00 | 13.30 | 0.00 | 26.70 | 40.00 | 0.00 | 13.30 | 0.00 |
Stage | M1 | M2 | M3 | M4 | Ms |
---|---|---|---|---|---|
Wr1A | 6.80 | 0.00 | 11.10 | 8.80 | 0.00 |
Wr1B | 11.40 | 2.40 | 3.70 | 10.50 | 2.70 |
CdA | 11.40 | 19.00 | 11.10 | 15.80 | 13.50 |
CdB | 11.40 | 0.00 | 11.10 | 7.00 | 8.10 |
Tr | 15.90 | 19.00 | 25.90 | 17.50 | 21.60 |
HtA | 15.90 | 33.30 | 25.90 | 17.50 | 45.90 |
HtB | 13.60 | 9.50 | 11.10 | 7.00 | 2.70 |
Wr2 | 13.60 | 14.30 | 0.00 | 15.80 | 5.40 |
All | 0.00 | 2.40 | 0.00 | 0.00 | 0.00 |
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Ramírez, S.; Zarzo, M.; García-Diego, F.-J. Multivariate Time Series Analysis of Temperatures in the Archaeological Museum of L’Almoina (Valencia, Spain). Sensors 2021, 21, 4377. https://doi.org/10.3390/s21134377
Ramírez S, Zarzo M, García-Diego F-J. Multivariate Time Series Analysis of Temperatures in the Archaeological Museum of L’Almoina (Valencia, Spain). Sensors. 2021; 21(13):4377. https://doi.org/10.3390/s21134377
Chicago/Turabian StyleRamírez, Sandra, Manuel Zarzo, and Fernando-Juan García-Diego. 2021. "Multivariate Time Series Analysis of Temperatures in the Archaeological Museum of L’Almoina (Valencia, Spain)" Sensors 21, no. 13: 4377. https://doi.org/10.3390/s21134377