Utafiti huu umetengeneza mbinu ya hatua mbili inayotegemea physics-informed neural networks kwa ajili ya kutabiri operative temperature ya ndani ya jengo la kihistoria la umma saa moja baadaye na matumizi ya umeme kwa madhumuni ya cooling. Physics-informed neural network ni mbinu ya machine learning inayoongeza mahusiano ya kimwili kama conservation of energy kwenye training loss function badala ya kujifunza tu patterns katika data za zamani.

Jengo la mfano la utafiti ni Royal Air Force 4. Regional Airspace Headquarters, pia linalojulikana kama ZAT Barracks, lililopo Bari, Italy na kujengwa mwanzoni mwa miaka ya 1930. Jengo hilo la ghorofa nne lenye jumla ya eneo la takribani 7559 m² linatumika leo kama public office. Ingawa kuta zake nene za tuff na concrete slabs hutoa thermal mass kubwa, thermal transmittance za kuta, paa na madirisha ni kubwa ikilinganishwa na vigezo vya sasa vya energy performance.

Utafiti haukutumia data set inayojumuisha direct continuous sensor measurements. Kwanza, building energy model iliundwa katika mazingira ya DesignBuilder–EnergyPlus kwa kutumia archival documents, on-site inspections, periodic measurements, user feedback na historical energy consumption. Baadaye, synthetic dataset ya samples 2208 ilizalishwa kutoka hourly simulation outputs za model hiyo kwa kipindi cha June–August.

Physics-informed neural network hufanya kazi katika hatua mbili mfululizo. Hatua ya kwanza hutabiri operative temperature saa moja baadaye kutokana na inputs kama current operative temperature, outdoor air temperature, solar gains, occupant-related internal gains, ventilation na cooling load. Hatua ya pili huunganisha predicted temperature na energy na usage inputs nyingine ili kukokotoa cooling electricity consumption saa moja baadaye.

Katika training ya neural network, si tofauti kati ya prediction na reference value pekee iliyotumika; residual ya building energy balance equation pia iliongezwa kwenye loss function. Hivyo lengo lilikuwa kufanya network iendane na synthetic data huku pia ikikaribia thermodynamic relation iliyofafanuliwa. Modeli hutumia hidden layers tano, neurons 256 kwa kila layer na hyperbolic tangent activation function. Adam na L-BFGS-B optimization methods zilitumika katika training, huku Optuna-based Tree-structured Parzen Estimator ikitumika katika uchaguzi wa physics coefficients.

Katika independent time-ordered test set, 0,091 °C RMSE, %0,34 CVRMSE, 0,025 °C MBE na %0,09 NMBE ziliripotiwa kwa operative temperature. Kwa cooling electricity consumption, RMSE ilikuwa 2,12 kWh, CVRMSE %9,95, MBE 0,04 kWh na NMBE %0,19. Thamani hizi zinaonyesha kwamba model iliweza ku-reproduce reference time series iliyotolewa na EnergyPlus kwa usahihi mkubwa.

Physics-informed model ilitoa hitilafu ndogo kuliko multilayer perceptron, Random Forest na linear regression models zilizotumika katika utafiti. Operative temperature RMSE iliripotiwa kupungua kwa %96,7–98,6, na cooling-consumption RMSE kwa %24,3–68,4, ikilinganishwa na models zilizolinganishwa.

Hata hivyo, performance hii haijathibitishwa dhidi ya continuously measured temperature na electricity data kutoka jengo halisi la kihistoria. Training na test targets zilitolewa kutoka EnergyPlus model ileile. Kwa hiyo utafiti hauonyeshi kwamba physics-informed network ilitabiri temperature ya jengo halisi kwa hitilafu ya 0,091 °C; unaonyesha kwamba network ilireproduce output ya simulation model inayodaiwa kuwa calibrated kwa hitilafu hiyo.

Pia kuna matatizo muhimu ya uwazi katika tathmini ya physical consistency ya chanzo. Units tofauti zimeunganishwa katika energy balance equations bila explicit conversion, standard deviation ya physics residual imeripotiwa kuwa takribani \(1{,}39\times10^8\) kW na bado deviations zimefasiriwa kuwa ndogo. Grafu zina negative cooling-consumption predictions na baadhi ya deviations kubwa ambazo ni vigumu kuoanisha na reported RMSE.

Kwa hiyo utafiti hautoi digital twin iliyothibitishwa na tayari kwa matumizi ya jengo halisi. Maelezo sahihi zaidi ni kwamba unaonyesha promising method demonstration iliyotengenezwa ili kuiga kwa haraka synthetic building-simulation data katika historic buildings na kutumia energy balance kama training regularizer.

Tathmini kwa mtazamo wa Türkiye: Historic public buildings, museums, administrative buildings, hans, mansions na registered buildings nchini Türkiye hukutana na conservation constraints zinazofanana wakati wa energy retrofit. Physics-informed models ni muhimu kwa kubadilisha building energy simulations kuwa prediction tools zinazofanya kazi haraka zaidi katika majengo ambako dense sensor placement haiwezekani. Hata hivyo, model iliyozalishwa kutoka jengo moja nchini Italy na kipindi cha summer pekee haiwezi kuhamishwa moja kwa moja kwenda Türkiye. Local climate, stone au brick type, window properties, shading, occupant behavior, HVAC system na conservation decisions lazima zifafanuliwe upya; matokeo lazima yathibitishwe kwa real meters na independent indoor sensors.

Swali kuu la utafiti ni lipi?

Swali kuu la utafiti ni kama operative temperature ya ndani saa moja baadaye na cooling electricity consumption vinaweza kutabiriwa katika historic building isiyo na continuous na comprehensive field data kwa kutumia neural network inayoungwa mkono na physical laws.

Watafiti walitafuta suluhisho kwa matatizo matatu makuu:

• Ufinyu wa sensor na energy data katika historic buildings,
• Uwezekano wa traditional machine learning models kutoa physically impossible results,
• Computational cost ya ku-run mara kwa mara detailed building energy models kama EnergyPlus kwa real-time control.

Suluhisho lililopendekezwa haliondoi detailed simulation kabisa. Kwanza EnergyPlus model hutumika kuzalisha training data, kisha neural network huwa faster surrogate model ya simulation hiyo.

Kwa nini energy prediction katika historic buildings ni ngumu?

Historic buildings, tofauti na modern buildings, hazina standardized materials na details. Stone, tuff, brick, timber, mortar na floor systems mahsusi kwa kipindi cha ujenzi huenda zisipatikane katika product catalogues za leo. Building layers zinaweza kuwa zimebadilishwa na interventions za baadaye, archival documents zimepotea au physical access kwa building elements imewekewa mipaka.

Conservation regulations pia hupunguza measurement na retrofit options. Kuweka sensor ndani ya ukuta, kubadilisha dirisha, ku-insulate facade au kufungua original surfaces kunaweza kuharibu historic value. Kwa hiyo detailed data collection ni ngumu na ghali zaidi kuliko katika modern office building.

Kwa upande mwingine, high thermal mass ya thick masonry walls husababisha outdoor air changes kufika indoors kwa kuchelewa. Occupancy, window opening, solar gain, equipment load na mechanical cooling zinapobadilika kwa wakati mmoja, nonlinear na time-delayed relationships hutokea kati ya operative temperature na energy demand.

Operative temperature ni nini?

Operative temperature ni thermal-comfort quantity inayowakilisha si indoor air temperature pekee bali pia athari ya mean radiant temperature kutoka surrounding surfaces. Kwa low air speeds, mara nyingi inaweza kufikiriwa kama weighted combination ya air temperature na mean radiant temperature.

Katika historic building, surface temperatures za thick walls na slabs zinaweza kutofautiana na indoor air temperature. Kwa hiyo air temperature pekee inaweza isieleze kikamilifu thermal environment inayohisiwa na occupants. Utafiti umetumia operative temperature kama target ya comfort prediction kwa sababu hiyo.

Physics-informed neural network ni nini?

Traditional neural network hujifunza statistical relationship kati ya inputs na target values. Modeli huchukuliwa kuwa successful kadiri prediction error inavyopungua wakati wa training. Hata hivyo, mbinu hii haihakikishi moja kwa moja physical constraints kama conservation of energy au heat transfer.

Katika physics-informed neural network, total loss hujumuisha sehemu mbili kuu:

\[ L_{\mathrm{total}} = \lambda_{\mathrm{data}}L_{\mathrm{data}} + \lambda_{\mathrm{physics}}L_{\mathrm{physics}} \]

Hapa:

• \(L_{\mathrm{data}}\), ni data error kati ya predicted value na reference value.
• \(L_{\mathrm{physics}}\), ni physics residual inayopima kiwango ambacho predictions zinapotoka kwenye defined energy-balance equation.
• \(\lambda_{\mathrm{data}}\) na \(\lambda_{\mathrm{physics}}\), ni relative weights za losses mbili katika training.

Lengo ni kuunda network ambayo si tu inakaribia reference data points, bali pia inatoa results zinazooana na physical equation iliyofafanuliwa.

Historic building gani ilichunguzwa katika utafiti?

Jengo la mfano ni ZAT Barracks lililopo kwenye pwani ya Bari. Lilijengwa mwanzoni mwa miaka ya 1930 kama Royal Air Force 4. Regional Airspace Headquarters na leo linatumika kama public office.

Kielelezo 3 kwenye ukurasa wa 7 wa utafiti kinaonyesha kwa pamoja location katika scales za Italy, Puglia na Bari, building placement kwenye satellite image na historic main facade facing the sea. Jengo lina symmetrical na monumental facade inayosisitizwa na towers mbili.

Thermal properties za building envelope ni zipi?

Thermal transmittance values za building elements zilijengwa upya kwa kutumia archival plans, visual inspections na standard thermophysical databases. Hakuna direct in-situ U-value test iliyofanywa kwa heat-flow measurement.

Kielelezo 4 kwenye ukurasa wa 8 kinaonyesha schematic sections za external wall, floor, roof na window layers pamoja na calculated thermal transmittances.

External walls na concrete slabs hutoa high heat-storage capacity. Total effective thermal capacity ilihesabiwa kwa uhusiano:

\[ C=\sum_i \rho_i c_{p,i}V_i \]

Hapa \(\rho_i\) ni material density, \(c_{p,i}\) specific heat capacity na \(V_i\) volume. Total effective thermal capacity iliyohesabiwa kwa jengo:

\[ C=1{,}1286\times10^9\ \mathrm{J/K} \]

imetolewa.

Heating, cooling na ventilation system iko vipi?

Heating hutolewa na diesel boiler yenye estimated seasonal efficiency ya takribani %85, black-steel distribution pipes na cast-iron radiators. Domestic hot water hutolewa na separate boiler circuit.

Variable-refrigerant-flow systems zilizozoned kwa floor hutumika katika cooling ya office areas. Katika energy model, nominal cooling coefficient of performance imewekwa 3,2.

Natural ventilation imeelezwa kuanza wakati indoor temperature iko kati ya 25–29 °C na outdoor air ni angalau 1 °C colder. Kwa air infiltration, value ya 0,8 h⁻¹ imetolewa katika main text.

Hata hivyo, ventilation values katika appendices hazioani:

Haijaelezwa kama values hizi zinawakilisha model zones tofauti, operating states tofauti au data-processing stages tofauti.

Training data ilizalishwaje?

Building geometry, envelope, occupant schedules, lighting, equipment loads, ventilation na HVAC properties zilimodeliwa katika DesignBuilder na calculations zikaendeshwa kwa EnergyPlus engine.

Hourly simulation ya June, July na August ilifanywa kwa kutumia IGDG climate data ya Bari-Palese. Kipindi cha miezi mitatu:

\[ 92\ \mathrm{gün}\times24\ \mathrm{saat}=2208\ \mathrm{saat} \]

kilizalisha data.

Data ziligawanywa katika sehemu mbili huku time order ikihifadhiwa:

Kuhifadhi time order ni sahihi kwa kuzuia future test data kuingia kwenye training set kupitia random shuffling. Hata hivyo, separate validation set haikutengwa. Haijaelezwa kwa undani jinsi Optuna ilivyofanya validation kwenye training data au jinsi overfitting ilivyodhibitiwa.

Matumizi ya synthetic data yanamaanisha nini?

Synthetic data ni data inayozalishwa na computational model badala ya kupimwa moja kwa moja na physical sensor. Katika utafiti huu, “reference” temperature na electricity values ambazo neural network inalenga zinatoka EnergyPlus simulation.

Mbinu hii hurahisisha development ya method kwa historic building ambako continuous measurement haiwezekani kwa sababu ya conservation constraints. Hata hivyo, neural network haijifunzi unknown behavior yote ya jengo halisi; inajifunza assumptions zilizocoded katika EnergyPlus model.

Kwa mfano, ikiwa occupant window-opening behavior, sensor error, VRF failure, maintenance deficiency, local shading, humidity effect au unexpected use change hazijaingizwa vizuri katika EnergyPlus model, neural network pia haitaweza kujifunza vitu hivyo.

Building energy model ilicalibrate vipi?

Kulingana na chanzo, building energy model ilicalibrate kwa kutumia natural-gas na electricity consumption za 2022–2024, archival documents, periodic temperature measurements na user feedback. ASHRAE Guideline 14–2023 na IPMVP Option D zimeripotiwa kufuatwa.

Hata hivyo, utafiti hauwasilishi kwa undani calibration evidence zifuatazo:

• Table ya measured na calculated monthly energy consumption,
• Monthly au hourly NMBE iliyopatikana kwa building energy model,
• CVRMSE iliyopatikana kwa building energy model,
• Comparison ya periodic indoor temperature measurements na simulation,
• Values za uncertain parameters kabla na baada ya calibration,
• Validation period ya calibration iliyo independent na training period.

Kwa hiyo, hata kama statement kwamba simulation inawakilisha jengo halisi kwa kutosha inakubaliwa, msomaji hawezi ku-evaluate upya goodness of fit hiyo independently kutoka published numerical results.

Hatua ya kwanza inatabiri operative temperature vipi?

Hatua ya kwanza hutumia thermal na environmental inputs katika muda \(t\) kutabiri operative temperature katika saa \(t+1\).

Kielelezo 6 kwenye ukurasa wa 10 wa utafiti kinaonyesha inputs kuu za hatua ya kwanza kama:

• Outdoor air temperature \(T_{\mathrm{out}}\),
• Natural ventilation na infiltration \(ACH\),
• Occupant-related internal gain \(Q_{\mathrm{occ}}\),
• Solar gain \(Q_s\),
• Sensible cooling load \(Q_{\mathrm{cool}}\),
• Current operative temperature \(T_o\),
• Effective thermal capacity \(C\),
• Total heat-transfer coefficient \(H\),
• Time na temperature-change derivatives.

Target variable imefafanuliwa kama:

\[ T_{o,t+1} \]

kama target.

Energy equation ya hatua ya kwanza ni ipi?

Equation iliyotolewa katika chanzo kwa temperature model ni:

\[ \alpha C\frac{\partial T_o}{\partial t} = \beta\left(Q_{\mathrm{cool}}+Q_s+Q_{\mathrm{occ}}\right) - \gamma H\left(T_o-T_{\mathrm{out}}\right)\partial t \]

Hapa:

• \(C\), ni effective thermal capacity.
• \(T_o\), ni operative temperature.
• \(Q_{\mathrm{cool}}\), ni cooling load.
• \(Q_s\), ni solar gain.
• \(Q_{\mathrm{occ}}\), ni occupant-related internal heat gain.
• \(H\), ni total heat-transfer coefficient ya building envelope.
• \(T_{\mathrm{out}}\), ni outdoor air temperature.
• \(\alpha\), \(\beta\) na \(\gamma\), ni scale coefficients zilizotuned kwa Optuna.

Katika chanzo, \(Q\) terms zimetolewa katika kWh, \(C\) katika J/K, \(H\) katika W/K na temperature derivative katika hourly time scale. Explicit conversion factors zinazobadilisha terms zote za equation kwenda common energy au power unit hazijaonyeshwa.

Zaidi ya hayo, final heat-loss term inaonekana kuzidishwa na \(\partial t\) katika chanzo. Haijaelezwa kama alama hii ni time integral, time step au typesetting error. Kwa hiyo equation kama ilivyoandikwa katika chanzo si dimensionally unambiguous.

Katika Table A.1, cooling load imetolewa kati ya −293,50 na 0 kWh. Katika equation, \(Q_{\mathrm{cool}}\) imeongezwa kwa gains nyingine kwa “plus” sign. Ikiwa negative value inatumika, inaweza kuwakilisha cooling kuondoa energy kutoka zone; hata hivyo sign convention haijafafanuliwa wazi katika maandishi.

Physics loss inatumikaje?

Total loss kwa operative-temperature model imefafanuliwa katika main text kama:

\[ L_{\mathrm{total}} = 0{,}8L_{\mathrm{data}} + 0{,}2L_{\mathrm{physics}} \]

\(L_{\mathrm{data}}\), ni mean squared error kati ya predicted na EnergyPlus-calculated temperature. \(L_{\mathrm{physics}}\), inategemea square ya residual inayobaki wakati network prediction inaingizwa kwenye energy equation.

Hata hivyo, Appendix A.5 inatoa loss weights za 0,5 data na 0,5 physics kwa model hiyo hiyo. Haiwezekani kuamua kwa uhakika kutoka chanzo ni weighting ipi ilitumika katika final results.

Optuna iliamua parameters zipi?

Kulingana na chanzo, trials 50 zilifanywa kwa Optuna inayotumia Tree-structured Parzen Estimator, kila trial ikitrainiwa epochs 500 na convergence ikipatikana mara nyingi ndani ya trials 20–25.

Main text inatoa \(\beta\) search range ya \(10^{-6}\)–\(10^{-2}\), huku Appendix A.4 ikitoa \(10^{-6}\)–\(10^{-3}\). Ingawa final value iko ndani ya ranges zote mbili, actual search space iliyotumika haiko wazi.

Maelezo ya kwanza ya method flow yanasema learning rate, number of layers na neurons pia zilikuwa optimized. Kwa upande mwingine, Appendix A.4 inasema wazi kwamba full architectural hyperparameter optimization haikufanywa.

Neural-network architecture iko vipi?

Taking average ya networks tatu inaweza kupunguza sensitivity kwa random initializations. Linear regression correction inayotumika baada yake hupunguza systematic bias.

Hata hivyo, haijaelezwa kama correction coefficient ilihesabiwa kwa training set pekee. Ikiwa test targets zilitumika, data leakage hutokea. Chanzo hakielezi wazi detail hii muhimu.

Hatua ya pili inatabiri cooling electricity consumption vipi?

Katika hatua ya pili, prediction ya \(T_{o,t+1}\) iliyozalishwa na network ya kwanza hutumiwa kama input mpya na cooling electricity consumption saa moja baadaye hukokotolewa:

\[ E_{\mathrm{el,cool},t+1} \]

Inputs za hatua hii zinajumuisha current na predicted operative temperature, temperature derivative, outdoor air temperature, solar gain, lighting, general lighting, equipment loads, HVAC fan power na air change.

Upper values za areal power densities zilizotolewa kwa lighting na equipment ni kubwa sana kwa historic office building. Haijaelezwa kama upper bounds hizi zimetokana na kugawanya whole-building totals kwa surface area au ni temporary variables kabla ya standardization.

Physics equation ya cooling model ni ipi?

Katika hatua ya pili, physical relation iliyotolewa katika chanzo ni:

\[ \alpha C\frac{\partial T_o}{\partial t} = \beta\left( Q_{\mathrm{cool}}+ Q_s+ Q_{\mathrm{occ}}+ Q_{\mathrm{vent}} \right) - \delta E_{\mathrm{el,cool}} \]

Katika equation hii, cooling-system COP imewekwa 3,2 na sensible cooling load imeunganishwa na electricity consumption.

Optimal scale coefficients:

zimeripotiwa.

Katika equation hii pia, left side ina dimensions za power, huku baadhi ya terms za right side na electricity consumption zikiwa katika kWh. Kwa sababu ya one-hour time step, energy na one-hour mean power zinaweza kuhusiana numerically; lakini chanzo hakionyeshi conversion hii wazi ndani ya equation.

Tatizo muhimu zaidi ni matumizi ya \(Q_{\mathrm{cool}}\) katika physics residual. Cooling electricity consumption tayari ni quantity inayoweza kuhesabiwa moja kwa moja kutoka sensible cooling load na COP. Ikiwa cooling load ya saa hiyo hiyo iliyotolewa na EnergyPlus imetumika katika physics loss, model inapata information iliyo karibu sana na target inayotakiwa kutabiri na partly deterministic. Haijaelezwa kama input hii itajulikana mapema katika real-time use.

Model ina mafanikio gani kwa operative temperature?

Kielelezo 7 kwenye ukurasa wa 12 kinaonyesha predicted na EnergyPlus-generated operative-temperature curves katika takribani saa 400 za test period. Lines mbili ziko karibu sana katika saa nyingi; tofauti huongezeka wakati wa rapid temperature changes na baadhi ya peaks.

Kwenye Kielelezo 8 ukurasa wa 13, predictions hukusanyika karibu na ideal 1:1 line. Kielelezo 9 kinaonyesha temperature residuals zikikusanyika karibu na zero.

Kulingana na maandishi, residuals:

• %79,7 zilibaki ndani ya ±0,10 °C,
• %99,73 zilibaki ndani ya ±0,5 °C

. Katika figure legend, ratio ya pili inaonekana %99,77. Tofauti hii ndogo haijaelezwa katika chanzo.

Limit ya ±0,5 °C imehusishwa na comfort tolerance katika utafiti. Hata hivyo, target ya model si actual occupant comfort vote, bali EnergyPlus operative temperature. Kwa hiyo result hii haimaanishi kwamba zaidi ya %99 ya occupants wako comfortable.

Model ina mafanikio gani kwa cooling consumption?

Kielelezo 10 kwenye ukurasa wa 14 kinaonyesha cooling consumption turning on/off na high-load periods katika takribani saa 400. Prediction curve hufuata general timing. Hata hivyo, katika baadhi ya low-load periods predictions zinaonekana kwenda chini ya zero.

Kwa sababu electricity consumption haiwezi kuwa negative physically, result hii inaonyesha kwamba positivity constraint haikutumika kwa model output. Haijaelezwa kama negative values ziliclipped hadi zero baada ya prediction.

Katika Kielelezo 11 kwenye ukurasa huohuo, ingawa points nyingi ziko karibu na 1:1 line, structures zifuatazo zinaonekana wazi:

• Vertical clusters za points katika low simulation values zilizopredictiwa takribani 45–60 kWh,
• Low clusters katika simulation values za 40–50 kWh zilizopredictiwa takribani 10–25 kWh,
• Points zinazotoka mbali na ideal line kwenye high-consumption extremes.

Ikiwa deviations za ukubwa huu ziko katika test set ileile ya points 442, haiwezekani kuthibitisha bila raw data jinsi zinavyoweza kuishi pamoja na RMSE ya 2,12 kWh. Chanzo hakielezi vya kutosha sample set iliyotumiwa na scatter plot na relationship yake na metric calculation.

Kwenye error heatmap ya ukurasa wa 15, average hourly errors za 8,3, 13,2, 14,3 na 30,2 kWh pia zinaonekana katika baadhi ya saa. Errors zimekusanyika hasa asubuhi na alasiri wakati load inaongezeka haraka.

Cooling demand na temperature huongezeka pamoja kila wakati?

Chanzo kimechunguza nyakati mbili maalum:

Chanzo kinatoa values hizi katika text kama “instantaneous power” kwa kW, lakini katika model target na tables kama kWh. Hourly energy na one-hour average power zinaweza kuwa numerically equal, lakini kutumia concepts hizi interchangeably huleta unit-clarity problem.

Cooling consumption kukaribia zero usiku huku temperature ikibaki relatively high imeelezwa kwa thermal inertia ya building na HVAC operating schedule. Observation hii inaonyesha kwamba high temperature si lazima iwe high cooling consumption kila saa.

Hata hivyo, utafiti unadai kwamba physics constraint hutenganisha causation na correlation. Neural network kutabiri time series mbili kwa usahihi hakuthibitishi causation yenyewe. Causality inahitaji intervention, controlled experiment au specific causal-inference design.

Physical consistency ilijaribiwaje?

Physical consistency ya model ilitathminiwa kwa distribution ya pointwise residuals za energy-balance equation. Kielelezo 13 kwenye ukurasa wa 15 kinaonyesha data na physics losses zikipungua katika epochs 3000.

Standard deviation ya physics residual ilihesabiwa kwa uhusiano:

\[ \sigma= \sqrt{ \frac{1}{N} \sum_{i=1}^{N} (r_i-\bar r)^2 } \]

Katika chanzo, result:

\[ \sigma=1{,}39\times10^8\ \mathrm{kW} \]

imetolewa. Horizontal axis ya Kielelezo 14 ukurasa wa 16 pia iko katika \(10^8\) scale, na legend inaonyesha takribani ±\(1{,}38\times10^8\) kW.

Value hii imefasiriwa na utafiti kama small deviation na indicator ya physical consistency. Hata hivyo, residual ya hundred million kilowatts ni orders of magnitude nyingi zaidi kuliko cooling demand ya jengo inayokadiriwa kuwa katika tens of kilowatts.

Possibilities zifuatazo hazijaelezwa katika chanzo:

• Residual inaweza kuwa imehesabiwa katika standardized au scaled space lakini ikawekewa unit isiyo sahihi,
• Conversion kati ya joule, watt, hour na kilowatt-hour inaweza kuwa haikutumika kikamilifu,
• Kunaweza kuwa na scientific-notation au unit-labeling error kwenye graph axis,
• Squared au scaled physics-loss value inaweza kuwa imewasilishwa kama physical power.

Mean ya residuals kuwa karibu na zero inaonyesha tu kwamba positive na negative errors zinabalance. Hii haithibitishi kwamba energy-balance error ni ndogo katika kila time step.

Zaidi ya hayo, kuwa na standard deviation katika distribution yoyote hakumaanishi moja kwa moja kwamba %68,27 ya values zitakuwa ndani ya ±1 standard deviation. Ratio hiyo ni valid tu chini ya normal-distribution assumption. Chanzo kimechukulia distribution kuwa approximately normal lakini hakijaripoti normality test.

PINN imefanikiwa kiasi gani kuliko traditional models?

Reported relative RMSE reductions za PINN zinaendana arithmetically na tables:

Hata hivyo, MLP, Random Forest na linear regression values katika comparison tables ni identical kwa njia isiyo ya kawaida kwa targets mbili tofauti. Kwa mfano, MLP RMSE ya 2,866 °C kwa temperature imerudiwa katika energy table kama 2,87 kWh; linear regression result ya 6,703 °C imerudiwa kama 6,70 kWh. CVRMSE, MBE na NMBE values pia zimerudiwa katika order ileile.

Kwa sababu scale, unit na time series za targets mbili ni tofauti kabisa, probability kwamba baseline models zote zitatoa error numbers zilezile ni ndogo. Hali hii ni possible reporting au table-copying issue inayohitaji re-check ya results.

Zaidi ya hayo, PINN hutumia average ya networks tatu na final linear correction, lakini haijaelezwa kama ensemble na correction procedures zilezile zilitumika kwa comparison models. MLP na Random Forest hyperparameters pia hazijatolewa kwa undani. Kwa hiyo haiwezi kuthibitishwa kwamba comparison ilifanywa chini ya fully equivalent model complexity.

Model kweli inahitaji data kidogo?

Utafiti unadai kwamba physics knowledge hupunguza data requirement. Hata hivyo, model ilitumia synthetic training data za saa 1766 na low-data experiments zifuatazo hazikufanywa:

• Kupunguza training data hadi %10, %25 au %50,
• Kulinganisha PINN na traditional models katika data quantities tofauti,
• Scenarios za kupunguza idadi ya sensors,
• Missing au noisy data experiments,
• Zero-shot transfer kwenda season au building nyingine.

Kwa hiyo utafiti unaonyesha kwamba physics-informed network imefanya vizuri zaidi katika simulation dataset iliyochunguzwa; hauonyeshi experimentally kwamba inahitaji data kidogo.

Model inaweza kuhamishwa kwenda historic buildings nyingine?

Chanzo kinadai kwamba inaweza kuadaptishwa kwenda historic structures nyingine kwa kubadilisha thermophysical inputs. Hata hivyo, network imefundishwa kwa building moja tu Bari na summer period moja.

Kwa transfer kwenda structure nyingine, angalau vipengele vifuatavyo vinahitaji kufafanuliwa upya:

• Building geometry na zoning,
• Wall, roof, window na floor layers,
• Thermal capacity na total heat-transfer coefficient,
• Climate data, solar orientation na shading,
• Occupant na equipment schedules,
• Natural-ventilation behavior,
• HVAC system na COP variation,
• New EnergyPlus calibration,
• Retraining ya physics coefficients na network.

Kwa hiyo utafiti haujaonyesha direct transfer kwa kubadilisha thermophysical numbers chache tu.

Digital twin na building-management-system use zinamaanisha nini?

Baada ya training, neural network inaweza kutoa predictions haraka zaidi kuliko detailed EnergyPlus simulation. Sifa hii inafanya matumizi ya model katika digital twin, building management system na model predictive control theoretically possible.

Kwa mfano, building management system inaweza kutabiri temperature na cooling demand saa moja baadaye na:

• Kuanza cooling kwa kiwango kidogo kabla ya peak hour,
• Kupunguza electricity peak demand,
• Kuchagua kati ya natural ventilation na mechanical cooling,
• Kuwajulisha managers kuhusu risk ya kutoka nje ya comfort range.

Hata hivyo, katika utafiti model haijaunganishwa na real building automation system, online prediction latency haijapimwa, na effect ya control commands kwenye energy au comfort haijajaribiwa experimentally.

Ni conclusions zipi zinazoungwa mkono na utafiti?

• PINN iliyofafanuliwa ilireproduce operative-temperature pattern katika EnergyPlus-derived test data kwa very low statistical error.
• Two-stage model iliweza kutumia temperature prediction kama input ya cooling-consumption prediction.
• General on, off na peak periods za energy-consumption time series zilikamatwa.
• Loss function inayotumia data na physics terms pamoja ilipungua wakati wa training.
• Numerical optimum set ya physics coefficients ilipatikana kwa Optuna.
• Model ilitoa lower errors kuliko comparison models zilizoripotiwa katika chanzo.
• Kwa sababu ya high thermal mass, peak times za temperature na cooling demand hazikulingana kila wakati.
• Kimetodolojia, trained network inaweza kutoa one-hour-ahead prediction bila rerunning simulation.

Utafiti hauthibitishi nini?

• Hauonyeshi kwamba operative temperature ya real building imetabiriwa kwa error ya 0,091 °C.
• Hauonyeshi kwamba real electricity meter imetabiriwa kwa error ya 2,12 kWh.
• Hauonyeshi kwamba model inadumisha performance ileile chini ya real sensor noise na occupant behavior.
• Hauonyeshi wazi kwamba physics constraint ni dimensionally correct na inazalisha small residual.
• Hauonyeshi kwamba model inazuia violations za actual energy conservation.
• Hauonyeshi kwamba negative energy predictions zimezuiwa.
• Haujaribu moja kwa moja kama PINN ni bora kuliko traditional models katika low-data condition.
• Hauthibitishi generalization kwenda building au climate nyingine.
• Hauonyeshi real-time digital twin au building-management-system implementation.
• Haupimi energy savings kutoka model predictive control.
• Hauonyeshi kwamba cooling-consumption prediction ni valid kwa mwaka mzima au heating season.
• Hauonyeshi kwamba conservation decisions au physical retrofit options zinaweza kuamuliwa automatically.

Ni nguvu gani za utafiti?

• Application problem iliyo wazi inayolenga data constraints za historic buildings imechaguliwa.
• Operative temperature na cooling consumption zimeshughulikiwa kama sequential targets mbili.
• Building geometry, envelope properties, HVAC na occupant schedules zimeunganishwa katika energy model moja.
• Data zimejaribiwa huku time order ikihifadhiwa bila random shuffling.
• Energy balance imeongezwa kwenye network training loss.
• Optuna-based physics-coefficient optimization imetumika.
• Ensemble prediction kutoka initializations tatu tofauti imetumika.
• CVRMSE, MBE na NMBE zimeripotiwa pamoja na RMSE.
• Time series, scatter, error distribution na hourly error heatmap zimewasilishwa.
• Authors wamekubali wazi kwamba model imewekewa mipaka na synthetic data.
• Data na code zimeripotiwa kuwa available upon reasonable request.
• Utafiti umechapishwa katika peer-reviewed open-access journal.

Ni vikwazo gani vya utafiti?

• Historic building moja tu imechunguzwa.
• June–August period pekee imemodeliwa.
• Model haijatrainiwa kwa real continuous field data.
• Test targets pia zinatoka EnergyPlus simulation.
• Building-energy-model calibration metrics hazijawasilishwa kwa undani.
• Hakuna in-situ U-value measurement.
• Energy-balance equations si dimensionally clear.
• Kuna additional \(\partial t\) notation katika temperature equation.
• Temperature derivative imeandikwa kwa reverse order katika text.
• Loss weights zimetolewa tofauti kama 0,8/0,2 na 0,5/0,5.
• Kuna inconsistencies katika Optuna search bounds.
• Maelezo yanatofautiana kuhusu kama architecture hyperparameters zilikuwa optimized.
• Hakuna separate validation set.
• Haiko wazi validation loss ilihesabiwaje.
• Ventilation ranges hazioani kati ya source sections.
• Operative-temperature ranges hazioani kati ya tables na plots.
• Cooling-model Optuna epoch counts zimetolewa tofauti.
• Three-network average na final linear correction huzuia performance kuhusishwa na physics constraint pekee.
• Haijaelezwa kama linear correction ilifikia test data.
• Detailed hyperparameters za comparison models hazijatolewa.
• Baseline-model error tables za targets mbili zina numbers zinazofanana kwa njia isiyo ya kawaida.
• Negative values zinaonekana katika cooling predictions.
• Cooling scatter plot haioani kikamilifu visually na reported RMSE.
• Standard deviation ya physics residual ni kubwa kupita kiasi kwa scale ya building.
• Unit au normalization conversion ya physics residual haijaelezwa.
• Production method ya %5–95 error band haijaelezwa.
• Uncertainty quantification haijafanywa.
• Data-reduction experiment ya low-data superiority haijafanywa.
• External validation katika building, climate au season nyingine haijafanywa.
• Digital-twin na control use ziko proposal level pekee.
• Data na code hazijachapishwa katika open repository, zimeachwa available on request.

Ni aina gani za majengo zinaweza kuchunguzwa Türkiye?

Mbinu inaweza kuchunguzwa Türkiye katika aina zifuatazo za majengo yenye limited continuous-monitoring infrastructure:

• Registered public buildings na administrative structures,
• Historic museums na archive buildings,
• Hans, caravanserais na traditional bazaar buildings,
• Stone au brick masonry school buildings,
• Historic mansions na cultural centers,
• Protected railway stations na military structures.

Kwa implementation, building-specific energy model lazima ijengwe kwanza kwa local building na kisha icalibrate kwa real measurements. Türkiye, billing data pekee haipaswi kuchukuliwa kuwa sufficient; angalau operative au air temperature katika orientations na floors tofauti, outdoor climate, HVAC operating status na main electricity consumption lazima zirekodiwe simultaneously.

Ni uthibitishaji gani unahitajika kwa adaptation Türkiye?

Umuhimu wake kwa past, present na future ni upi?

Hapo awali, energy analysis ya historic buildings ilifanywa hasa kwa steady-state calculations au detailed lakini slow dynamic simulations. Data scarcity na conservation constraints zilifanya real-time prediction systems kuwa ngumu kuanzisha.

Mchango wa sasa ni kuhamisha behavior ya detailed building-energy model kwenda neural network inayofanya kazi haraka na kutumia energy balance kama training regularizer. Mbinu hii ina potential ya kutoa fast one-hour-ahead predictions badala ya rerunning simulation.

Katika future, method inahitaji retraining kwa real sensor na meter data, dimensional correction ya physics equations, calculation ya uncertainty intervals, external validation katika historic buildings tofauti na measurement ya actual energy savings katika building-control system.

Mbinu na Matokeo ya Utafiti

Muhtasari wa kiufundi wa research design

Error metrics zilihesabiwaje?

Mean bias error:

\[ MBE= \frac{1}{n} \sum_{i=1}^{n} (P_i-O_i) \]

Normalized mean bias error:

\[ NMBE= \frac{ \sum_{i=1}^{n}(P_i-O_i) }{ n\bar O } \times100 \]

Root mean square error:

\[ RMSE= \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (P_i-O_i)^2 } \]

Coefficient of variation of RMSE:

\[ CVRMSE= \frac{RMSE}{\bar O} \times100 \]

Hapa \(P_i\) ni model prediction, \(O_i\) EnergyPlus reference value, \(\bar O\) reference mean na \(n\) number of samples.

Utafiti umetaja NMBE limit ya ASHRAE Guideline 14 ya ±%10 na CVRMSE limit ya %30 kwa hourly model evaluation. Hata hivyo, thresholds hizi kimsingi ni za calibration ya energy models dhidi ya measured data. Low error ya PINN katika kureproduce simulation model ileile haimaanishi kwamba building energy model yenyewe imethibitishwa tofauti dhidi ya real building.

Detailed comparison ya operative-temperature results

PINN result iko karibu sana na simulation reference. Hata hivyo, RMSE ya takribani 2,8 °C kwa MLP na Random Forest ni kubwa kuliko inavyotarajiwa kwa hourly prediction problem ambapo input–target relationship kati ya current temperature na one-hour-ahead temperature inapaswa kuwa strong. Kwa kuwa settings za comparison models, lagged-temperature inputs na training performance hazijatolewa, chanzo cha tofauti hii kubwa hakiwezi kutathminiwa.

Detailed comparison ya cooling-consumption results

Kwamba rows za MLP, Random Forest na linear regression ni rounded versions tu za values katika temperature table ni moja ya editorial issues muhimu zaidi zinazohitaji validation katika results table.

Methodological inconsistencies ndani ya chanzo

Matokeo yanayoonekana kutoka figures zenyewe

Balanced interpretation ya findings

Result imara zaidi ya utafiti ni kwamba large two-stage feed-forward network inaweza kuiga hourly temperature na cooling patterns zinazozalishwa na EnergyPlus. Operative-temperature curve ya model iko wazi karibu na reference simulation.

Ingawa success katika cooling consumption ni limited zaidi, general on–off schedule na load trends zimekamatwa. Hata hivyo, scatter plot, negative values na high hourly errors zinaonyesha kwamba performance haiwezi kufupishwa kikamilifu na RMSE number moja.

Label ya “physics-informed” inategemea kuongeza residual ya energy balance kwenye loss function. Kwa sababu ya equation units, scale ya physics residual na inconsistencies katika source, haiwezi kuhitimishwa kwamba model imethibitishwa thermodynamically. Maelezo ya tahadhari zaidi ni neural network iliyoregularize kwa physical relations.

Real application value ya utafiti iko katika idea ya kubadilisha detailed building simulation kuwa fast surrogate model. Ili kuthibitisha potential hii katika field conditions, model inahitaji kujaribiwa dhidi ya real measurements, different buildings na unseen climate conditions.

Maelezo ya Chanzo na Mbinu

Jina kamili la asili la utafiti: Physics-Informed Neural Networks for predicting indoor temperature and cooling demand in historic buildings

Waandishi na mpangilio sahihi: Simona Semeraro; Francesca Vecchi; Roberto Stasi; Umberto Berardi.

Equal first author: Hakuna taarifa ya equal contribution au equal first authorship.

Mwandishi anayewajibika: Umberto Berardi.

Anwani ya mawasiliano: umberto.berardi@poliba.it

Taasisi: ArCoD – Department of Architecture, Construction, and Design, Polytechnic University of Bari, Bari, Italy.

DOI:10.1016/j.jobe.2025.114392

Kiungo rasmi cha chanzo:Ukurasa rasmi wa makala wa ScienceDirect

Jarida: Journal of Building Engineering.

Volume: 115.

Article number: 114392.

Mwaka wa uchapishaji: 2025.

Mchapishaji: Elsevier Ltd.

Tarehe ya submission: 29 Mayıs 2025.

Tarehe ya revised version: 30 Eylül 2025.

Tarehe ya acceptance: 13 Ekim 2025.

Tarehe ya online publication: 24 Ekim 2025.

Peer-review status: Peer-reviewed scientific research article.

Open-access status: Open access chini ya CC BY 4.0 license.

Idadi ya kurasa: 27.

Aina ya chanzo: Research article inayojumuisha dynamic building-energy simulation inayodaiwa kuwa calibrated, synthetic-data generation, physics-informed neural network, hyperparameter optimization na machine-learning comparison.

Michango ya waandishi:

• Simona Semeraro: Methodology, investigation, formal analysis, data curation na conceptualization.
• Francesca Vecchi: Formal analysis, data curation na conceptualization.
• Roberto Stasi: Formal analysis, data curation na conceptualization.
• Umberto Berardi: Funding acquisition, formal analysis, data curation na conceptualization.

Ufadhili: Support ilitolewa na study ya “Digital twin nella gestione di vettori energetici nuovi per l’accoppiamento edificio-trasporti in ambito urbano” ndani ya National Center for Sustainable Mobility project, iliyofadhiliwa na Italian Ministry of University and Research chini ya National Recovery and Resilience Plan. Project code imetolewa kama CUP D93C22000410001.

Mgongano wa maslahi: Waandishi wametangaza kutokuwa na known financial interest au personal relationship inayoweza kuathiri utafiti.

Data access: Simulation dataset inayojumuisha hourly operative temperature, cooling energy na processed training inputs imeripotiwa kuwa obtainable kutoka kwa corresponding author upon reasonable request.

Code access: PINN architecture, hyperparameters na Optuna optimization scripts zimeripotiwa kushirikiwa on request kwa research purposes. Hakuna public na permanent code-repository link iliyotolewa.

Main tools used: DesignBuilder, EnergyPlus, Python-based machine-learning tools, StandardScaler na Optuna.

Makala hii ya Kiswahili imeandaliwa baada ya kuchunguza main text, appendices, energy-balance equations, data tables, building-envelope schematics, neural-network workflows, time series, error distributions, physics-residual plots na model comparisons za utafiti. Hakuna external scientific results zisizopatikana katika study zilizoongezwa. External-source check ilitumika tu kuthibitisha official bibliographic identity, journal record, DOI na publication status ya utafiti.

Matokeo ya utafiti hayaonyeshi kwamba physics-informed network ilitabiri real-building measurements kwa hitilafu ileile. Prediction targets ni synthetic data zilizozalishwa na EnergyPlus model inayodaiwa kuwa calibrated. Kwa hiyo reported errors zinawakilisha simulation–neural-network agreement.

Main technical transparency issues za source ni unit mismatch katika energy equations, additional \(\partial t\) katika temperature equation, derivative expression iliyoandikwa reversed, differing loss weights, differing Optuna ranges, validation-set uncertainty, ventilation-range inconsistencies, differing epoch counts, repeated error values katika baseline-model tables, negative cooling predictions na physics residual ya takribani \(10^8\) kW.

Utafiti unaunga mkono kwamba neural networks zenye physical regularization zinaweza kuwa fast surrogate models kwa historic-building simulations. Real field accuracy, low-data superiority, transferability kwenda buildings nyingine, real-time digital-twin use na energy savings bado hazijathibitishwa.