A New Method for Simultaneous Determination of the TDC Offset and the Pressure Offset in Fired Cylinders of an Internal Combustion Engine

Transcription

1 energies Article A New Method for Simultaneous Determination of the Offset and the Pressure Offset in Fired Cylinders of an Internal Combustion Engine Urban Žvar Baškovič *, Rok Vihar, Igor Mele and Tomaž Katrašnik Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia; rok.vihar@fs.uni-lj.si R.V.; igor.mele@fs.uni-lj.si I.M.; tomaz.katrasnik@fs.uni-lj.si T.K. * Corresondence: urban.zvar-baskovic@fs.uni-lj.si; Tel.: Academic Editor: Chang Sik Lee Received: 13 December 2016; Acceted: 16 January 2017; Published: 23 January 2017 Abstract: An innovative comutationally efficient method for the simultaneous determination of to dead centre offset and ressure offset is resented. It is based on characteristic deviations of the rate of heat release ROHR that are secific for both offsets in comression hase and exansion hase after the end of combustion. These characteristic deviations of the ROHR are derived from first rinciles and they were also confirmed through manual shifts of the ressure trace. The ROHR is calculated based on the first law of thermodynamics using an in-cylinder ressure trace, engine geometrical arameters and oerating oint secific arameters. The method can be alied in off-line analyses using an averaged ressure trace or in on-line analyses using a single ressure trace. In both alication areas the method simultaneously determines the osition and the ressure offset within a single rocessing of the ressure trace, whereas a second refinement ste can be erformed for obtaining more accurate results as correction factors are determined more accurately using nearly converged inut data. Innovative analytic basis of the method allows for significant reduction of the comutational times comared to the existing methods for the simultaneous determination of offset and ressure offset in fired conditions. The method was validated on a heavy-duty and a light-duty diesel engine. Keywords: internal combustion engine; thermodynamic analysis; offset; ressure offset; offset correction algorithm 1. Introduction Reduction of exhaust emissions and simultaneous maintenance or even increasing of engine efficiency and secific ower is a major challenge for engine manufacturers. In addition to the well-established emission measurement rocedures, in 2017 EU lans to introduce real driving emission tests to tackle the well-known issue of laboratory tests not accurately reflecting the amount of emissions emitted during real driving conditions [1]. Moreover, real driving emission tests will aly also to the vehicles in service [2]. To comly with these requirements, manufacturers are focusing on controlling combustion rocess with various strategies, which need to be sufficiently robust also for vehicles in service featuring comonents that are subjected to wear and ageing. One of the very romising strategies to aroach the otima with resect to exhaust emissions and engine efficiency is the closed-loo combustion control CLCC using in-cylinder ressure sensors. CLCC thus adats injection strategies according to the actual in-cylinder ressure trace and arameters that are derived thereof while considering also arameters from other engine sensors. In-cylinder ressure is measured with high-frequency ressure transducers, which are often based on the iezoelectric technology. These sensors offer short resonse times but they do not Energies 2017, 10, 143; doi: /en

2 Energies 2017, 10, of 22 deliver the absolute ressure readings. Therefore, a referencing rocedure called egging, which was an object of research in many studies [3 11], needs to be alied. Generally, methods can be divided into two grous. The first grou deends on additional sensors and consists of methods that reference measured ressure signal to the ressure measured in the intake [3,4,7,11,12] or the exhaust manifold [8,11] during the intake or the exhaust rocess. The second grou consists of methods that determine ressure offset with numerical algorithms from data gathered during the high-ressure hase of the engine cycle [3,5,9 11,13]. Among them, two oint referencing method and least-squares method achieve accuracy of about ±0.25 bar as reorted in [3]. Three oint referencing method, linear least-squares method with 15 referencing oints and non-linear least-squares method with 15 referencing oints achieve accuracy of about ±0.15 bar as reorted in [5], whereas three oint referencing method with five-oints averaging achieves accuracy of about ±0.1 bar [5]. Conclusion of a study [11], erformed at /min, while comaring various manifold referencing methods and olytroic referencing methods, was that manifold referencing worked best for the exerimental conditions, however olytroic referencing would be suerior at higher engine seeds. In a study reorted in [7], where inlet manifold ressure referencing and olytroic index ressure referencing methods were comared, it was determined that agreement of aroximately ±0.12 bar was achieved. Although many of the numerical methods for determining the ressure offset are based on the in-cylinder ressure of the fired engine [3,5,10,11,13], the osition has to be known in order to acquire accurate results. Determination of the correct absolute angle reresents a vital iece of information for calculating the volume of the combustion chamber, which is needed for evaluation of indicated work and combustion arameters. An error of 1 CA in osition can cause u to 10% evaluation error for indicated mean effective ressure IMEP and u to 25% error for the total heat released during the combustion [14]. Methods for determining the offset can be divided into two main grous. The first grou reresents methods suorted with additional hardware, while the second one is based on the algorithms that determine the osition on the basis of the indicated in-cylinder ressure as a function of the crank angle osition. The osition can be determined using a dedicated caacitive sensor that is generally inserted into the sark lug or injector hole. In both cases, the measured cylinder has to be motored combustion is not resent and therefore this method cannot be used during normal engine oeration. It is not feasible to equi high volume series roduction engines with very accurate sensors for determination of the absolute ressure and of the osition. The second grou consists of thermodynamic methods that are based on the indicated in-cylinder ressure. These methods can further be divided into the methods that are alicable for motored and for fired cycles. Majority of the methods are develoed for the motored cycles. The simlest but also in general the least accurate method with accuracy of about ±1 CA is setting the osition to the osition where the indicated motored ressure reaches its eak [15]. Other numerical methods determine osition based on the ressure trace symmetry [15], on the olytroic exonent values [16,17], on a definition of a loss angle that is related to the energy and mass losses [18], on a ressure curve symmetry in combustion and exansion hases on fixed intervals [15], on the heat loss ower through the combustion chamber wall [19], on the correlation between IMEP, the maximum cylinder ressure and the hase lag [20] and on the unsymmetrical characteristics of the ressure diagram [21]. These methods feature different accuracies, which are in addition to the selected method deendent also on the engine tye and on the quality of the ressure signal. In general, it can be reviewed from the literature that methods based on a definition of a loss angle can achieve accuracy below ±0.1 CA [18], which is similar to the methods based on the olytroic exonents [17] or heat release shaing [19], whereas method based on an unsymmetrical characteristics of the ressure diagram can achieve accuracy below 0.05 CA [21]. In [15], it was reorted that IMEP based calibration method achieved the smallest error between estimated and actual osition of of CA. However, such a good agreement was achieved as the same engine cycle was used for calibration of model arameters and also for analysis and thus this aroach is not alicable for real engine

3 Energies 2017, 10, of 22 oeration. In general, all methods alicable for motored cycles feature limited alicability, as they cannot be alied during fired oeration of the engine. The literature offers only a few methods for determination of the under fired conditions. Ref. [22] resented a method based on rate of heat release calculation, which can aroach accuracy of the olytroic exonent method. It needs to be mentioned that ressure offset needs to be determined accurately to aroach errors listed reviously in this aragrah. Alternatively, in [23] a methodology for determination of total comression ratio and errors of the ressure and the offset was resented. The method is based on the olytroic aroach and it features multile case secific arameters. Furthermore, method features moderate accuracy of 1 CA if the aroximation interval ends earlier than 165 CA and u to 0.05 CA in the cases where combustion starts after. This characteristic of the method is related to the fact that the method was develoed for shi engines, where these limitations can be acceted, whereas in the automotive engines it is in general not ossible to aly aroximation intervals that allow for achieving high accuracy with the roosed method. From the review of the existing literature, it can be summarized that desite availability of methods that are dedicated to determine either the absolute ressure or the osition, to the best of authors knowledge, accurate and generally alicable analytically based methods for simultaneous determination of the and the ressure offset based on the in-cylinder ressure of fired engine are not available. Therefore, if both arameters are unknown, iterative rocedures of both adations are generally alied using the comression hase of the ressure trace, which is common in commercial software tools. However, results of the iterative aroach for determination of and ressure offsets do not necessarily assure convergence to the correct values because of co-deendency of both searched arameters in the comression hase. To address this issue, an innovative analytically based method for simultaneous determination of the ressure and the offset based on the in-cylinder ressure trace of the fired engine is elaborated in this aer. The method is based on characteristic deviations of the rate of heat release ROHR that are secific for the and the ressure offset in comression and exansion hase. For a secific offset, ROHR in comression and exansion hase namely features deviation with the same sign, where the sign of ROHR deviations in comression and exansion hase changes for a secific ressure offset. These characteristic deviations of the ROHR are derived from first rinciles thus forming analytic basis for correcting both offsets. The method is thus comutationally very efficient and allows for determination of both offsets within a single calculation, whereas a second refinement ste can be done for obtaining more accurate results as correction factors are determined more accurately using nearly converged inut data. There are numerous alications where osition and ressure offset need to be determined simultaneously. These alications go beyond automotive segment, which will be the main focus of this aer, and cover also the segment of large engines, where on-line erformance monitoring is one of the imortant measures to ensure roer engine oeration. 2. 0D Thermodynamic Framework 2.1. ROHR Analysis Pressure traces can be used to calculate various thermodynamic arameters, where besides indicated work, ROHR evaluated using the 0D thermodynamic framework is one of the most valuable arameters for combustion analysis. Commonly ROHR is related to the heat released during the combustion eriod, whereas in diesel engines negative ROHR values before the start-of-combustion indicate fuel evaoration. In an ideal case, ROHR would be zero in the entire comression and exansion hase. This would have been achieved, if the following assumtions would be fulfilled: - Pressure trace is measured without any errors and disturbances,

4 Energies 2017, 10, of 22 - Pressure trace is ositioned correctly with resect to the absolute ressure value and the osition - Pressure trace is rocessed with the thermodynamic model yielding no discreancies to the actual heat transfer, gas roerties, fuel evaoration and blow-by. In general, this is not the case esecially during the resence of and ressure offsets. Therefore, in this study, the term ROHR in equations denoted as dq/ will be used as indication of the energy imbalance not only during combustion and otential evaoration but in the entire high-ressure hase of the engine cycle. In addition, the term exansion hase will be used for the eriod between the end-of-combustion and exhaust valve oening and the term comression will be used for the eriod between the intake valve closing and start of injection in diesel engines or sark initiation in sark ignited engines. Using the 0D thermodynamic framework, which is similar to the formulations found in classic textbooks, e.g., [24], ROHR is given as: where: and: dq base = 1 + R A 1 u dv + +m u + T C A u u T A u A = 1 + T R C = 1 R dλ dm + m u u λ T R λ R A 1 d dh dq ht, are to be inserted into Equation 1. Equation 1, which resents general equation for evaluation of the ROHR, includes terms that are deendent on volume derivative 1 + R A 1 u dv, in-cylinder mass derivative u A T u dm u u, relative air-fuel ratio derivative m λ T R λ dλ R A, in-cylinder ressure derivative m u + T C A u d, enthaly flux in and out of the combustion chamber dh/ and heat flux from the gas within the combustion chamber dq ht /. With the aim to allow code orting on the real-time hardware and esecially the FPGA Field rogrammable gate array chi the comutational effort was reduced. Therefore only most significant gas roerty deendencies were considered in further analyses and thus u/ and R/ were assumed zero because of small deendencies of the ressure on the internal energy u and the secific gas constant R at temeratures lower than aroximately 2700 K [25]. This aroach can additionally be reasoned by the fact that methodology is demonstrated on comression ignition engines generally featuring lower averaged in-cylinder temeratures comared to sark ignition engines. However, it should be noted that analyses resented in the aer could be done using Equation 1 and that all findings resented in the aer are also valid under consideration of gas roerty deendencies given in Equation 4. As only high ressure hase of the cycle is analysed and as blow-by is very small in modern well maintained engines, dh is also set to zero to minimize comutational effort, whereas again analyses resented in the aer could be done using Equation 1 and findings resented in the aer do not alter based on the consideration of the blow-by. Considering listed assumtions, Equation 1 can be reformulated to: dq = 1 + RA 1 u dv + u T A u R R m dm + u λ T u R λ R A dλ + m T C A u d dq ht

5 Energies 2017, 10, of 22 A general equation for calculating the heat flux from the in-cylinder charge to the combustion chamber walls has a form: n dq ht = α S i T i T, 5 i=1 where α reresents heat transfer coefficient, T charge temerature, T i temeratures of the surrounding walls liner, cylinder head, iston and S i surface area or the surrounding walls. For heat transfer coefficient calculation, emirical correlations are generally used, e.g., [24,26]. Proosed, 0D thermodynamic framework is comatible with any heat transfer coefficient correlation, whereas results are resented for the Hohenberg model [27]. Detailed derivation for this secific heat transfer coefficient correlation are resented in Aendix A ROHR Analysis in Comression and Exansion Phases Innovative method for simultaneous determination of the and the ressure offset is based on the integral values of the ROHR in comression and exansion hases. As combustion hase is not considered in the correction algorithms, Equation 4 can be further simlified as mass variation, which is characteristic for fuel injection in diesel engines, is not resent in comression and exansion hases. In addition, change of chemical comosition is generally related to either combustion or evaoration, which are both not resent in comression and exansion hase of the diesel engines if it is required to consider evaoration in the comression hase of secific engines, corresonding terms of the Equation 4 need to be retained. Equation 4 can thus be further simlified to: dq = R A u dv T C + m A u d dq ht. 6 It can be noted at this oint that the roosed method is imlemented in a way that the thermodynamic analysis is erformed using Equation 4 in a more general case it could also be Equation 1, whereas derivatives of Equation 6 that are resented in Section 2.3 are used to calculate correction factors for the and the ressure offset, while using secies comosition and temerature inuts calculated by Equation ROHR Integral Values Deending on the Pressure and Offsets The main idea of the innovative method for simultaneous determination is based on characteristic deviations of the ROHR that are secific for the and the ressure offset in the comression hase and the exansion hase. To derive these deendencies, Equation 6 is exanded in the Taylor series with the resect to the ressure offset δ and the angle deviation δ and the linear terms were retained. For the ressure offset series exansion yields: dq δ = R A u dv δ + R A dv u δ Heat transfer term in the Equation 7 is exanded as: + V C R A d u δ δ dqht. 7 δ dq ht = S h T h δα S h T δα S h δt α + S l T l δα S l T δα S l δt α + S i T i δα S i T δα S i δt α, 8 where: δt = V δ. 9 m R and subscrits h, l, i reresent head, liner and iston, resectively. Full derivation of the Equation 8 for the Hohenberg heat transfer coefficient correlation is given in Aendix A.

6 Energies 2017, 10, of 22 Partial derivative of internal energy with resect to temerature, resent in the Equation 7, is defined as: u δ = u u T0 + δt, λ 0 T 0, λ 0, 10 where T 0 and λ 0 reresent arameters, calculated with estimated absolute ressure, and δt is evaluated by Equation 9. Table 1 rovides a basic insight into contributions of articular terms in Equation 7 to the δdq/ for ressure offset of 1 Pa arbitrary selection for illustration uroses and for different crank angle ositions. R A dv δ u The following notation is used: is denoted as b; V C R A d δ u R A u dv δ is denoted as a; is denoted as c and δdq ht/ is denoted as d. Sign of the term a is in the comression and the exansion hase determined by the value of dv/ and it thus features negative values in comression hase, whereas in exansion hase it features ositive values. Terms b and c feature oosite signs, which is related to different signs of dv/ and d/ in the comression and the exansion hase. Their absolute sum is comarable to the absolute value of term d, which is two orders of magnitude lower than the magnitude of the term a. Therefore it can be concluded that the term a most significantly influences the ROHR for a given ressure offset in the entire region excet around the, whereas these regions are generally not of interest for analyses of fired cycles. As the sum of all terms and thus the δdq/ is mainly driven by the term a it also features oosite signs in comression and exansion hase. Table 1. Values of terms deendent on ressure offset. Angle CA Term a Term b Term c Term d Sum Combining Equations 8 10 along with the Equation A3 from Aendix A into Equation 7, yields a linear deendency between dq/, i.e., left hand side of Equation 7, reresenting the dq/ deviation due to the ressure offset at a articular crank-angle osition, and the ressure offset δ, which can be reresented as: dq δ = k δ, 11 where k reresents the roortionality arameter derived by right hand side of Equation 7. Similar rocedure as for the ressure offset can also be erformed for the offset, δ. Equation 12 was derived from Equation 5, while the influence of the terms δ, δ u/, δ / and δt, deendent on offset were considered in the equation: δ dq = δ u The term δ is defined as: R A u dv δ V C R A u δ d d δ R A dv δ u + V C R A d. 12 δ dqht = d ϕ 0+δ d ϕ 0, 13 where ϕ 0 reresents correct crank angle without offset for each ressure measurement.

7 Energies 2017, 10, of 22 In a similar manner as in the derivation of the δdq/, the term δt is defined as: and the term δ u/ as: u δ δt = V m R δ, 14 = u T 0 + δt, λ 0 u T 0, λ Table 2 rovides, similarly as the Table 1, insight into magnitudes of the terms of the Equation 12, which were evaluated for the offset value of 1 CA arbitrary selection for illustration uroses 1 and for different crank angle ositions. The following notation is used: R A u dv δ is denoted as 1 a; R A dv δ u as d; V C R A u δ δ δϕ is denoted as b; dv δ is denoted as c; V C R A d δ u is denoted is denoted as e and δdq ht/ is denoted as f. The most influential term is term e, which is directly deendent on δd/, which features same signed values in comression and exansion hase of the engine cycle excet around the. This can be related to the fact that as given in Equation 13, δd/ features the same sign as the second derivative of ressure with resect to the crank-angle, which is due to basic characteristic of the olytroic rocess and iston kinematics ositive in comression and exansion hase excet around the. The sum of all terms and thus the δdq/ therefore follows the trend of the term e, i.e., δdq/ features the same sign in the comression and exansion hase. Results in Tables 1 and 2 that were derived from Equations 7 and 12 resectively thus confirm the basic hyothesis of the roosed method stating that ROHR features different characteristic deviations in the comression hase and the exansion hase when subjected to the ressure and the offset. Table 2. Values of terms deendent on the offset. Angle CA Term a Term b Term c Term d Term e Term f Sum Combining Equations along with the Equation A5 from Aendix A, again gives linear deendency between dq/, i.e., left hand side of Equation 12, and the offset δ: dq δ = k δ, 16 where k reresents the roortionality arameter derived by right hand side of Equation 12. In general, the and the ressure offset are not known and thus the framework for simultaneous determination of both offsets is generated by summing Equations 11 and 16. To minimize the imact of uncertainties of the ressure signal on the accuracy of the roosed method, the method does not rely on the single values of sloe coefficients k and k evaluated at a articular crank-angle osition, but it rather relies on the integrated values of k and k over a re-secified intervals in the comression and the exansion hase. Likewise, to reduce the imact of uncertainties on the δdq/ and δdq/ these values are not taken at a articular crank-angle osition, but they are integrated over the same re-secified intervals. Summing of Equations 11 and 16 and integration over re-secified intervals in the comression and the exansion hase thus yields:

8 Energies 2017, 10, of 22 I com = com I ex = ex δ δ dq dq + δ dq = k com δ + k com δ = k com, δ + k com, δ, + δ dq = k ex δ + k ex δ = k ex, δ + k ex, δ, where I com and I ex reresent integral values of the ROHR when subjected to arbitrary combination of the and the ressure offset in comression com and exansion ex resectively and k com,, k com, and k ex,, k ex, reresent integrals of k and k over the same intervals in the comression and the exansion hases. In Section 2.1 it was stated that in an ideal case, which besides others imlies also zero and ressure offset, the values of I com and I ex would be zero. By assuming that values of I com and I ex are more influenced by the and the ressure offset than by the deviations caused by the thermodynamic framework for their rocessing, it is ossible to ascribe most of the deviations of I com and I ex from zero to the and ressure offset. This assumtion might be artially justified by the fact that a sohisticated version of the 0D thermodynamic framework is used in Section 2, whose validity and robustness in this or very similar level of fidelity is demonstrated in multile research and industrial studies. Moreover, in subsequent sections, it will be shown that the roosed method yields very accurate results although ROHR of the ressure trace with zero and ressure offset features moderate deviations from zero as discernible in figures of Section 4, which more adequately resembles real alication area of the method and roves its robustness. Values of I com and I ex at unknown and ressure offset are thus simly calculated by integrating the Equation 4 in a more general case it could also be Equation 1 re-secified intervals in the comression and the exansion hase. Similarly, the values of k com,, k com, and k ex,, k ex, are calculated by integrating Equations 11 and 16 over the same intervals, while using secies comosition and temerature inuts calculated by Equation 4 as indicated in Section 2.2. All arameters of Equations 17 and 18 are thus calculated during the rocessing of the ressure trace. Simultaneous determination of the and the ressure offset is afterwards erformed by solving of the Equations 17 and 18, i.e., the linear system of two equations with two unknowns. Due to limited additional workload of integrating I com and I ex dq/ is often integrated in comression and exansion hase of resents codes and thus these two arameters can be calculated just by simle subtractions as well as k com,, k com, and k ex,, k ex, and solution of the linear system with two equations, the method is very comutationally efficient and thus suitable also for low comuting ower systems and real time systems. 3. Exerimental Setu and Procedure 3.1. Exerimental Setu Two significantly different diesel engines were selected to demonstrate general alicability of the develoed numerical method for determination of the and the ressure offset. First engine was a 4-cylinder, 4-stroke, turbocharged, 1.6 L light-duty diesel engine PSA, Paris, France featuring a common rail fuel system. Its main characteristics are resented in Table 3. The second engine was a 6-cyliner, 4-stroke, turbocharged 6.87 l heavy-duty diesel engine MAN Grou, Munich, Germany the characteristics of which are resented in Table 4. Pressure was indicated with a resolution of 0.1 CA with an AVL GH12D iezo-electric ressure transducer AVL LIST GmbH, Graz, Austria, which was connected to the AVL MICROIFEM charge amlifier and voltage signal was measured with a 16 bit, four channel National Instruments Cororation Austin, TX, USA data-acquisition system with maximum samling frequency of 1 MS/s/ch. For the ressure indication, external trigger was rovided by a CAM UNIT Tye 2613B Kistler Instrumente GmbH, Sindelfingen, Germany

9 Energies 2017, 10, of 22 Table 3. PSA engine characteristics. Engine PSA DV6ATED4 Cylinders 4, inline Dislacement 1560 cm 3 Bore/stroke 75/88.3 mm Comression ratio 18:1 Maximum ower /min Maximum torque /min Table 4. MAN engine characteristics. Engine MAN D 0826 LOH 15 Cylinders 6, inline Dislacement 6870 cm 3 Bore/stroke 108/125 mm Comression ratio 18:1 Maximum ower /min Maximum torque /min 3.2. Method First, the alication of the roosed method in office or off-line analyses will be resented. In this tye of analyses averaged and filtered in-cylinder ressure trace is rocessed. In the literature, there are many averaging and filtering techniques available for rearing a suitable ressure trace for reliable thermodynamic analysis. Therefore, the re-rocessing ste includes selection of the number of cycles that are used for averaging and selection of the filtering technique and its arameters. Averaging is imortant to suress the cycle to cycle variations. This rocedure not only diminishes signal noise but also allows for achieving higher consistency between the measured arameters like fuel mass flow and air mass flow in the averaged cycle. In general, increased number of cycles that are used for averaging is favoured, however there is a oint over which increasing the number of cycles does not lower standard deviation between cycles. Therefore, 100 consecutive cycles were used for averaging of the ressure trace, which is in between the roosed minimum 50 cycles [28] and few hundred cycles [11]. Filtering was erformed with digital equirile finite imulse resonse FIR filter. Pass-band and sto-band frequencies of the digital FIR filter were defined using a Fourier transformation [29]. The ass-band and sto-band frequencies were determined with discrete Fourier transform DFT in the region between the frequencies that are mainly the result of the iston kinematics and combustion and the frequencies of first eigen resonance sectra occurrence. The validation of the acquired transition bands was erformed with short-time Fourier transform STFT analysis and transition bands were corrected if needed. After defining the above re-rocessing stes, the offline rocedure comrises the following stes that can be groued into the baseline and the refinement ste. The baseline ste comrises: 1. Pressure signal averaging. 100 consecutive cycles were used for averaging in this analysis. 2. Pressure signal filtering. Low-ass filtering rocedure with equirile FIR filter was alied in this analysis. 3. Calculation of sloe coefficients. k com, and k ex, are calculated with the Equations and k com, and k ex, are calculated with Equations 7 11 as resented in Section Calculation of ROHR integrals. Integral values of ROHR for comression and exansion regions are calculated using Equation 6 and denoted as I com and I ex.

10 Energies 2017, 10, of Determination of the and ressure offsets. Using k com,, k com,, k ex, and k ex, as well as I com and I ex, determined in items 3 and 4, ressure and offset values are calculated using Equations 17 and 18. As coefficients in item 3 were calculated with shifted ressures traces their values deviate from the values that would have been calculated for zero and ressure offset. Therefore, a second refinement ste can be erformed to further imrove accuracy of the results. This refinement ste comrises: 6. Shift the ressure trace for the and the ressure offset determined in item Performing stes 3 to 5 to obtained refined values of the and the ressure offset. In general, it is ossible to iterate on stes 6 and 7 until convergent offset values are calculated, however in none of the erformed analyses there was a need for more than the baseline and one refinement ste. The roosed method is alicable also in on-line analyses and it is demonstrated in the aer that it is ossible to aly the roosed method on a single filtered in-cylinder ressure trace, which in combination with low comutational effort of the method allows for udate rates on the cycle-to-cycle basis. The only difference between the off- and on-line methods is absence of ressure cycle averaging in the on-line method, whereas the filter setting might also differ between these two alications. Also filters with orders of several hundred are alicable for the on-line analysis as order of 100 results in only 5 CA delay when using crank angle resolution of 0.1 CA. During test on the FPGA integrated circuit the calculation times in the range of 1 ms were achieved for the entire thermodynamic analysis resented in Section 2.1. A basic ste of the and ressure offset algorithm consumes aroximately 20% of the CPU time of the thermodynamic calculation. Overall comutational times below 2 ms therefore allow for real-time alicability of the method. The alied Virtex-5 LX50 FPGA integrated circuit Xilinx Inc., San Jose, CA, USA was integrated into National Instruments ComactRIO reconfigurable chassis 9114 and was running with the frequency of 40 MHz. 4. Results and Discussion 4.1. Qualitative Validation of the ROHR for the Pressure and Offset In this section, ROHR deviations will be analysed for different ressure and offsets to rovide exerimental evidence on the hyotheses that ROHR features different characteristic deviations in the comression hase and the exansion hase when subjected to the and the ressure offset. It might be worth noting that the results in this section were calculated by alying Equation 4, which is commonly used in ROHR analyses, and equations roosed in Sections 2.2 and 2.3 were not used to generate any of the results in this section. For this demonstration urose, re-rocessed ressure traces of the PSA DV6ATED4 engine with accurately determined ressure and osition, which was measured with the caacitive sensor, were subjected to redetermined manual offsets in the and the ressure. Presented ressure traces were averaged over 100 consecutive cycles and filtered with low-ass FIR filter. Figure 1 shows the ressure trace with accurately determined ressure and osition denoted as Original and ressure traces which were subjected to shifts of ±1 and ±3 CA in the oerating oint at /min and 100 Nm. In the Figure 2 ROHR values calculated using Equation 4 are resented. Vertical red lines in comression and exansion regions reresent selected integration intervals used in Equations 17 and 18, which will be ket constant for all cases in the resented aer. Integration interval in the comression hase is from 70 to 40 CA, whereas in exansion hase it is from 90 to 120 CA.

11 Energies 2017, 10, of 22 Energies 2017, 10, 143 Energies 2017, 10, of of 22 a b a b Figure 1. a offset variations ±1, 3 CA of the ressure trace with resect to the crank angle at Figure 1. a offset variations ±1, 3 CA of ofthe ressure trace with resect to the crank angle at /min and 100 Nm; b detailed view /min and 100 Nm; b detailed view. a b a b Figure 2. a ROHR curves of the offset variations ±1, 3 CA deendent of crank angle at /min Figure Figure and a a Nm; ROHR ROHR b curves curves detailed of of view. the the offset offset variations variations ±1, ±1, 3 CA CA deendent deendent of of crank crank angle angle at at /min 1/min and and Nm; Nm; b b detailed detailed view. view. It can be observed in Figure 1 that for a ositive offsets, ROHR curves feature negative It can be observed in Figure 1 that for a ositive offsets, ROHR curves feature negative values in It can the be comression observed inand Figure the exansion 1 that for ahase, ositive whereas offsets, an inverse ROHR trend curves is observed feature negative for negative values values in the comression and the exansion hase, whereas an inverse trend is observed for negative in the offsets. comression This observation and theconfirms exansion results, hase, resented whereasin anthe inverse Table trend 2 for crank is observed angles for in comression negative offsets. This observation confirms results, resented in the Table 2 for crank angles in comression and offsets. exansion This observation hases. confirms results, resented in the Table 2 for crank angles in comression and and exansion hases. exansion Similarly hases. for the offset, the Original ressure trace was also subjected to the ressure Similarly as for the offset, the Original ressure trace was also subjected to the ressure offset variations, Similarly as where for the Original offset, ressure the Original trace was ressure shifted trace by ±0.5 was and also ±1 subjected bar. Results, to the resented ressure offset variations, where the Original ressure trace was shifted by ±0.5 and ±1 bar. Results, resented in offset the Figures variations, 3 and where 4, were theacquired Original ressure with the trace Equation was shifted 4 for different by ±0.5 and ressure ±1 bar. offsets. Results, Unlike resented for in the Figures 3 and 4, were acquired with the Equation 4 for different ressure offsets. Unlike for the in the Figures variation, 3 and where 4, were a acquired offset resulted with thein Equation ROHR deviation 4 for different with the ressure same sign offsets. in comression Unlike for the the variation, where a offset resulted in ROHR deviation with the same sign in comression and exansion variation, regions, whereit acan be offset observed resulted that infor ROHR a ressure deviation offset with variation, the same ROHR signcurves in comression feature and exansion regions, it can be observed that for a ressure offset variation, ROHR curves feature deviations and exansion with different regions, it signs can be in observed comression thatand for aexansion ressure offset regions, variation, which ROHR coincides curves with feature the deviations with different signs in comression and exansion regions, which coincides with the results deviations from the withtable different 1. signs in comression and exansion regions, which coincides with the results results from the Table 1. from Figures the Table 2 and 1. 4 thus in addition to the governing equations in Section 2.3 and results generated Figures 2 and 4 thus in addition to the governing equations in Section 2.3 and results generated thereof Figures confirm 2 the andbasic 4 thus hyothesis in additionof tothe theroosed governing method equations stating Section that ROHR 2.3 and features resultsdifferent generated thereof confirm the basic hyothesis of the roosed method stating that ROHR features different characteristic thereof confirm deviations the basic in hyothesis comression of thehase roosed and the method exansion statinghase that ROHR when subjected features different to the characteristic deviations in the comression hase and the exansion hase when subjected to the characteristic and the ressure deviations offset. inthis the comression further roves hase the hyothesis and exansion that, considering hase when assumtion subjected stated to the and the ressure offset. This further roves the hyothesis that, considering assumtion stated after Equation and the ressure 18 in Section offset. This 2.3, further it is ossible roves the to determine hyothesisboth that, offset considering simultaneously assumtionusing stated after Equation 18 in Section 2.3, it is ossible to determine both offset simultaneously using Equations after Equation 17 and in by Section knowing 2.3, itrohr is ossible integrals to determine comression both offset and simultaneously exansion hases using and Equations values Equations 17 and 18 by knowing ROHR integrals in comression and exansion hases and values of 17,,,,, and,. of and 18,, by knowing,, ROHR, and integrals,. in comression and exansion hases and values of k com,, k com,, k ex, and k ex,.

12 Energies 2017, 10, of 22 Energies 2017, 10, of 22 Energies 2017, 10, of 22 a b a b Figure 3. a Pressure offset variations ±0.5, bar deending on the crank angle at /min and 100 Figure 3. a Pressure offset variations ±0.5, 1 1bar bar deending on on the the crank crank angle angle at 2000 at /min 1/min and and Nm; Nm; b detailed b detailed view. Nm; b detailed view. view. a b a b Figure 4. a ROHR curves of the ressure offset variations ±0.5, bar deendent of crank angle at Figure Figure /min a a and ROHR ROHR 100 Nm; curves curves b of of detailed the the ressure ressure view. offset offset variations variations ±0.5, ±0.5, 1 bar bar deendent deendent of of crank crank angle angle at at /min 1/min and and Nm; Nm; b b detailed detailed view. view Quantitative Validation of the ROHR for the Pressure and Offset 4.2. Quantitative Validation of the ROHR for the Pressure and Offset 4.2. Quantitative Validation of the ROHR for the Pressure and Offset In Section 4.1 it was roven that by manual shifting of ressure traces the same trends as In Section 4.1 it was roven that by manual shifting of ressure traces the same trends as redicted In Section by Equations 4.1 it was roven 7 and that 12 by manual is reroduced. shifting of To ressure validate traces the the analytical same trends framework as redicted also redicted by Equations 7 and 12 is reroduced. To validate the analytical framework also by quantitatively, Equations 7 it and is necessary 12 is reroduced. to comare To the validate values theof analytical and framework values also calculated: quantitatively, a by ithe is quantitatively, it is necessary to comare the values of and values calculated: a by the necessary integrating toequations comare the 11 values and 16 of I com over and the I ex intervals values calculated: secified in a Section by the4.1 integrating denoted Equations as analytical 11 integrating Equations 11 and 16 over the intervals secified in Section 4.1 denoted as analytical and aroach 16 over and the b by intervals integrating secified Equation in Section 6 over 4.1 the denoted same interval as analytical for ressure aroach traces and that b were by aroach and b by integrating Equation 6 over the same interval for ressure traces that were integrating subjected to Equation redetermined 6 overmanual the sameoffsets interval for the ressure and traces the ressure that were of subjected the original to redetermined ressure trace subjected to redetermined manual offsets in the and the ressure of the original ressure trace manual as exlained offsets in insection the 4.1 and denoted the ressure as numerical of the original aroach. ressure Results trace are as shown exlained for three in Section oerating 4.1 as exlained in Section 4.1 denoted as numerical aroach. Results are shown for three oerating denoted oints of as the numerical PSA DV6ATED4 aroach. engine Results at an are engine shown seed for three of 2000 oerating 1/min and oints torques of theof PSA 20 Nm, DV6ATED4 100 Nm oints of the PSA DV6ATED4 engine at an engine seed of /min and torques of 20 Nm, 100 Nm engine and 160 atnm. an engine This analysis seed ofis 2000 besides 1/min validation and torques of the of 20 roosed Nm, 100aroach Nm and 160 imortant Nm. This also analysis to rove is and 160 Nm. This analysis is besides validation of the roosed aroach imortant also to rove besides that first validation order exansion, of the roosed which was aroach used in imortant Section 2.3, alsois tosufficient rove that to first obtain order high exansion, fidelity results. which that first order exansion, which was used in Section 2.3, is sufficient to obtain high fidelity results. was In the used Figures in Section and 2.3, 6, iscomarison sufficient tobetween obtain high numerical fidelity results. and analytical In the Figures calculation 5 andof 6, comarison ROHR as In the Figures 5 and 6, comarison between numerical and analytical calculation of ROHR as a between function numerical of offset and and analytical ressure calculation offset is resented of ROHR as for acomression function of and offset exansion and ressure regions. offset It can function of offset and ressure offset is resented for comression and exansion regions. It can is be resented observed for that comression in all figures andanalytical exansionand regions. numerical It can be results observed nearly thatcoincide, all figures which analytical roves be observed that in all figures analytical and numerical results nearly coincide, which roves and adequacy numerical of the results roosed nearly aroach coincide, for which the roves and adequacy ressure offsets the roosed in comression aroach and for exansion the adequacy of the roosed aroach for the and ressure offsets in comression and exansion and regions ressure of the offsets engine incycle. comression and exansion regions of the engine cycle. regions of the engine cycle.

13 Energies 2017, 10, of 22 Energies 2017, 10, of 22 Figure 5. Values of the I com and I ex deending on offset variation. Figure Figure Values of of the I on com and I ex deending on ressure offset variation.

14 Energies 2017, 10, of 22 It is worth noting that coefficients k com,, k com, and k ex,, k ex, in Equations 17 and 18 can also be determined by manually shifting the ressure traces as resented in this section. However, this method is not ursuit in this aer due to the two deficiencies. First, to calculate coefficients k com,, k com, and k ex,, k ex, using the numerical method it is necessary to first obtain the ressure trace with zero and ressure offset. This means that the final result is needed to initiate the method, which is not lausible. Unlike, for the analytical method the coefficients are calculated during the rocessing of the ressure trace, as elaborated in the next section, and exact values of the and ressure offset are not needed in this calculation. Second, also under the assumtion that the and ressure offset are known the analytical method is more comutationally efficient as equations for determining the coefficients k com,, k com, and k ex,, k ex, are evaluated and integrated only in a very limited range, whereas additional rocessing of the entire cycles is needed in the numerical method Validation and Discussion The roosed rocedure was validated on a four cylinder light-duty PSA diesel engine and on a six cylinder heavy-duty MAN diesel engine introduced in Section 3.1. Tests were erformed in a way that a full factorial matrix of re-rescribed shifts in for [ 3, 1, 0, 1, 3] CA and in ressure [ 100,000, 50,000, 0, 50,000, 100,000] Pa was alied to the original ressure trace. Afterwards, both off- and on-line method was alied to evaluate the offsets and accuracy of the results was analysed by comarison to the re-rescribed shifts PSA Engine Accuracy of the off-line aroach was tested first and the results are summarized in Table 5 for the oerating oint at /min and 100 Nm. Results of additional oerating oints are resented in Aendix B. To rove convergence of the method and to rove that in all analysed case on both engines mostly a baselined and one refinement ste, i.e., two iterations, are needed, stes 6 and 7 resented in Section 3.2 were called in a loo with re-secified exiting criteria. Calculation was considered converged when and ressure offset values did not change more than 0.05 CA and 1000 Pa, resectively, between two iterations. The number of iterations needed to reach the accuracy threshold is given in Table 6. It can clearly be seen that not more than two iterations, i.e., a baselined and one refinement ste, are needed to reach converged solution with tight convergence limits, whereas in multile oints only a single calculation was sufficient. As converged solution does not necessary imly that the solution is also accurate, it is imortant to analyse the absolute errors in the and the ressure offsets given in Table 5. It can be seen that the largest error in ressure corrections is less than 1300 Pa and less than 0.06 CA for correction, which roves high accuracy of the results. In cases where comression ratio is not correctly known, the accuracy of the method diminishes due to an error in the calculation of the cylinder volume and its derivative. To quantify this effect, sensitivity analysis was erformed for the oerating oint at /min and 100 Nm with off-line aroach. It was determined that an error in comression ratio of ±0.5 results in error in determining absolute ressure of less than ±4500 Pa and correction of less than ±0.2 CA. Table 5. Calculated ressure and offsets and their absolute errors for the PSA engine and oerating oint /min and 100 Nm using the off-line method. Calculated Pressure Offset 100,000 98,899 99,526 98,784 98,728 99,211 50,000 48,841 49,526 48,784 48,728 49, ,000 51,159 50,474 51,216 51,272 50, , , , , , ,789

15 Energies 2017, 10, of 22 Table 5. Cont. Calculated Offset 100, , , , Absolute Difference Pressure Offset 100, , , , Absolute Difference Offset 100, , , , Table 6. Number of iterations for the PSA engine and oerating oint /min and 100 Nm using the off-line method. 100, , , , Additionally, also accuracy of the on-line alication was analysed and the results analogue to those for the off-line alication are resented in the Tables 7 and 8. For this analysis, one of the arbitrary selected ressure traces out the set of the 100 cycles used for off-line analysis was alied. The ressure trace was filtered using the same FIR filter with the same settings as in the off-line case were alied to exose influence of the averaging on the accuracy of the results. Likewise, the same convergence criteria as for the off-line case were alied in this on-line case. It can be seen that all errors in ressure offset are lower than 2000 Pa and that and errors in the offsets are lower than 0.27 CA. Desite exected lower accuracy of the results comared to the off-line case, it can be concluded that accuracy of the results is good considering the fact that only a single ressure trace was rocessed. Table 7. Calculated ressure and offsets and their absolute errors for the PSA engine and oerating oint /min and 100 Nm using the on-line method. Calculated Pressure Offset 100, , , , , ,565 50,000 51,286 51,883 51,986 51,946 51, ,000 48,714 48,117 48,014 48,054 48, ,000 98,714 98,117 98,014 98,054 98,435

16 Energies 2017, 10, of 22 Table 7. Cont. Calculated Offset 100, , , , Absolute Difference Pressure Offset 100, , , , Absolute Difference Offset 100, , , , Table 8. Number of iterations for the PSA engine and oerating oint /min and 100 Nm using the off-line method. 100, , , , MAN Engine Furthermore, the method was validated on the heavy-duty diesel engine, which highly differentiates from PSA engine in size and other secifications, to validate its universal alicability. Results, calculated with the offline aroach for simultaneous and ressure offset determination are resented in the Table 9 for oerating oint at /min and 373 Nm. Table 9. Calculated ressure and offsets and their absolute errors for the MAN engine and oerating oint /min and 373 Nm using the off-line method. Calculated Pressure Offset 100,000 99,287 99,747 99,133 99,237 99,366 50,000 49,279 50,082 49,136 49,237 49, ,000 50,721 49,918 50,864 50,763 50, , ,721 99, , , ,634 Calculated Offset 100, , , ,

17 Energies 2017, 10, of 22 Table 9. Cont. Absolute Difference Pressure Offset 100, , , , Absolute Difference Offset 100, , , , General conclusions for heavy-duty engine are similar to the ones of the light-duty engine in terms of accuracy of the and the ressure offset correction as well as in terms of number of iterations. In Table 9, highest absolute difference of the ressure offset and the offset reach 866 Pa and 0.06 CA, resectively. Therefore, also for the heavy duty engine case, calculated and ressure offsets are determined with high enough accuracy in no more than two iterations, as resented in the Table 10. It can therefore be concluded that the methodology is alicable on various engine tyes. Table 10. Number of iterations for the MAN engine and oerating oint /min and 373 Nm using the off-line method. 100, , , , Conclusions In this aer an innovative method for simultaneous determination of offset and ressure offset from ROHR integrals in comression and exansion regions of the high-ressure hase of engine cycle was develoed and validated with two different size four-stroke diesel engines, which verifies its alicability to light- and heavy-duty engines. The method relies on a thermodynamic model that calculates ROHR curve and its deendency on and ressure offsets from ressure trace, geometric data and oerating oint secific arameters. It is resented in the aer that the roosed method is alicable on averaged filtered in-cylinder ressure trace and also on filtered non-averaged, i.e., single, ressure trace making it suitable for off- and on-line analyses resectively. Exectedly, accuracy of the results is higher when averaged ressure traces are used, where in all analysed cases accuracy in deranging the ressure offset is better than 1300 Pa and accuracy of the offset is better than 0.06 CA. However, also when single ressure traces is used the accuracy of the method is still very high as resented in the Table 7. Irresective of the alied ressure trace, converged results are obtained in most two iterations of the method. Therefore the method can be considered as very comutationally efficient featuring comutational times of few milliseconds on the FPGA integrated circuits. Author Contributions: Urban Žvar Baškovič and Tomaž Katrašnik develoed the method for simultaneous determination of the offset and the Pressure Offset in Fired Cylinders of an Internal Combustion Engine; Urban Žvar Baškovič and Rok Vihar erformed measurements, on which the method was validated; Urban Žvar Baškovič, Rok Vihar and Igor Mele imlemented the method and calculated all thermodynamic arameters and other data, resented in the article; Urban Žvar Baškovič and Tomaž Katrašnik wrote the article.

18 Energies 2017, 10, of 22 Conflicts of Interest: The authors declare no conflict of interest. Nomenclature A model arameter / C model arameter / H enthaly J k com, ; k ex, roortionality arameter J/Pa k com, ; k ex, roortionality arameter J/ CA m charge mass kg in-cylinder ressure Pa Q released energy J R secific gas constant J/kg K S surface m 2 T temerature K u secific internal energy J/kg V combustion chamber volume m 3 λ relative air-fuel ratio / ϕ angle CA Subscrits and Abbreviations 0 at correct and offset values 0D zero-dimensional base base derivation CLCC closed-loo combustion control CA crank angle com comression ex exansion FPGA field rogrammable gate array FIR finite imulse resonse h cylinder head ht heat transfer i combustion chamber walls IMEP indicated mean effective ressure l liner ressure offset i iston ROHR rate of heat release to dead centre offset to dead centre Aendix A Hohenberg heat transfer model: α = 130 V T 0.4 c m , A1 where V,, T reresent charge roerties volume, ressure and temerature, resectively and c m denotes mean iston seed. Linearised Hohenberg heat transfer model for ressure offset: δα = 130 V 0.06 c m V δ m R 5. A2

19 Energies 2017, 10, of 22 Heat transfer for ressure offset: δ dqht = HTCF A h T h 130 V 0.06 c m δ 5 A V h T δα A h c m V 2 δ m R A l T δ 5 A l δt α + A i T i 130 V 0.06 c m V V 0.06 c m m R V 0.4 m R m R δ α + A l T l 130 V δ 5 A i T δα A i V m R δ α A3 Linearised Hohenberg heat transfer model for offset: δα = 130 V 0.06 c m V ϕ 0+δ ϕ 0. A m R 5 Heat transfer for offset: δ dqht = HTCF A h T h 130 V 0.06 c m V m R 2 ϕ 0+δ ϕ 0 5 A h T δα A h m R V ϕ 0+δ ϕ 0 α + A l T l 130 V 0.06 c m V 2 ϕ m R δ ϕ 0 5 A l T 130 V 0.06 c m V m R 2 ϕ 0+δ ϕ 0 5 A i δt α + A i T i 130 V 0.06 c m V m R 2 ϕ 0+δ ϕ 0 5 A i T δα A i V m R δ α A5 Aendix B Following tables resent results of and ressure offset calculation for the additional PSA engine oerating oints. Table B1. Calculated ressure and offsets and their absolute errors for the PSA engine and oerating oint /min and 20 Nm using the off-line method. Calculated Pressure Offset 100,000 99,724 99,936 99,347 99,310 99,788 50,000 49,652 49,936 49,347 49,310 49, ,000 50,348 50,064 50,653 50,690 50, , , , , , ,212 Calculated Offset 100, , , ,

20 Energies 2017, 10, of 22 Table B1. Cont. Absolute Error Pressure Offset 100, , , , Absolute Error Offset 100, , , , Table B2. Number of iterations for the PSA engine and oerating oint /min and 20 Nm using the off-line method. 100, , , , Table B3. Calculated ressure and offsets and their absolute errors for the PSA engine and oerating oint /min and 20 Nm using the off-line method. Calculated Pressure Offset 100,000 99,263 99,827 99,977 99,916 99,392 50,000 48,996 49,827 49,977 49,916 49, ,000 51,004 50,173 50,023 50,084 50, , , , , , ,608 Calculated Offset 100, , , , Absolute Error Pressure Offset 100, , , , Absolute Error Offset 100, , , ,

21 Energies 2017, 10, of 22 Table B4. Number of iterations for the PSA engine and oerating oint /min and 20 Nm using the off-line method. 100, , , , References 1. Euroean Commission. Commission Welcomes Member States Agreement on Robust Testing of Air; Euroean Commission: Brussels, Belgium, Euroean Commission. Draft of Commision Regulation as Regards Emissions from Light Passenger and Commercial Vehicles Euro 6; Euroean Commission: Brussels, Belgium, Lee, K.; Yoon, M.; Sunwoo, M. A study on egging methods for noisy cylinder ressure signal. Control Eng. Pract. 2008, 16, [CrossRef] 4. Klein, M.; Eriksson, L.; Åslund, J. Comression ratio estimation based on cylinder ressure data. Control Eng. Pract. 2006, 14, [CrossRef] 5. Fanelli, I.; Camoreale, S.M.; Fortunato, B. Efficient On-Board Pegging Calculation from Piezo-Electric Sensor Signal for Real Time In-Cylinder Pressure Offset Comensation. SAE Int. J. Engines 2012, 5, [CrossRef] 6. Al-Durra, A.; Canova, M.; Yurkovich, S. A real-time ressure estimation algorithm for closed-loo combustion control. Mech. Syst. Signal Process. 2013, 38, [CrossRef] 7. Brunt, M.F.J.; Pond, C.R. Evaluation of Techniques for Absolute Cylinder Pressure Correction; SAE Technical Paer ; SAE International: New York, NY, USA, Lim, B.; Lim, I.; Park, J.; Son, Y.; Kim, E. Estimation of the Cylinder Pressure in a SI Engine Using the Variation of Crankshaft Seed; SAE Technical Paer ; SAE International: New York, NY, USA, Leonhardt, S.; Norbert, M.; Isermann, R. Methods for Engine Suervision and Control Based on Cylinder Pressure Information. Mechatronics 1999, 4, [CrossRef] 10. Müller, N.; Isermann, R. Control of Mixture Comosition Using Cylinder Pressure Sensors; SAE Technical Paer ; SAE International: New York, NY, USA, Randolh, A.L. Methods of Processing Cylinder-Pressure Transducer Signals to Maximize Data Accuracy; SAE Technical Paer ; SAE International: New York, NY, USA, Lee, K.; Cho, S.; Kim, N.; Min, K. A study on combustion control and oerating range exansion of gasoline HCCI. Energy 2015, 91, [CrossRef] 13. Verschaeren, R.; Schaedryver, W.; Serruys, T.; Bastiaen, M.; Vervaeke, L.; Verhelst, S. Exerimental study of NOx reduction on a medium seed heavy duty diesel engine by the alication of EGR exhaust gas recirculation and Miller timing. Energy 2014, 76, [CrossRef] 14. Piitone, E.; Beccari, A. Reliable osition determination: A comarison of different thermodynamic methods through exerimental data and simulations. In Proceedings of the 17th SAE Brasil International Mobility Technology Congress Exosition, Sao Paulo, Brazil, 7 9 October Nilsson, Y.; Eriksson, L. Determining Position Using Symmetry and Other Methods Rerinted From: Modeling of Sark Ignition Engines. In Proceedings of the 2004 SAE World Congress, Detroit, MI, USA, 8 11 March Hribernik, A. Statistical Determination of Correlation Between Pressure and Crankshaft Angle During Indication of Combustion Engines; SAE Technical Paer ; SAE International: New York, NY, USA, Stas, M.J. Thermodynamic Determination of T.D.C. In Piston Combustion Engines; SAE Technical Paer ; SAE International: New York, NY, USA, Piitone, E.; Beccari, A. Determination of in internal combustion engines by a newly develoed thermodynamic aroach. Al. Therm. Eng. 2010, 30, [CrossRef]

22 Energies 2017, 10, of Tunestål, P. Offset Estimation from Motored Cylinder Pressure Data based on Heat Release Shaing. Oil Gas Sci. Technol. 2011, 66, [CrossRef] 20. Pinchon, P. Calage thermodynamique du oint mort haut des moteurs à iston. Oil Gas Sci. Technol. 1984, 39, [CrossRef] 21. Wang, X.B.; Deng, K.Y.; He, F.Z.; Zhou, Z.H. A thermodynamics model for the comression and exansion rocess during the engine s motoring and a new method for the determination of with simulation technique. Al. Therm. Eng. 2007, 27, [CrossRef] 22. Chang, H.; Zhang, Y.; Chen, L. An alied thermodynamic method for correction of in the indicator diagram and its exerimental confirmation. Al. Therm. Eng. 2005, 25, [CrossRef] 23. Polanowski, S. Determination of location of To Dead Centre and comression ratio value on the basis of shi engine indicator diagram. Pol. Marit. Res. 2008, 15, [CrossRef] 24. Heywood, J.B. Internal Combustion Engine Fundamentals; McGraw-Hill Book Co.: Singaore, Chase, M. NIST-JANAF Thermochemical Tables; American Chemical Society: Washington DC, USA; American Institute of Physics for the National Institute of Standards and Technology: Woodbury, NY, USA, Wimmer, A.; Pivec, R.; Sams, T. Heat Transfer to the Combustion Chamber and Port Walls of IC Engines Measurement and Prediction; SAE Technical Paer ; SAE International: New York, NY, USA, Hohenberg, G.F. Advanced Aroaches for Heat Transfer Calculations; SAE Technical Paer ; SAE International: New York, NY, USA, Ceviz, M.A.; Çavuşoğlu, B.; Kaya, F.; Öner, İ.V. Determination of cycle number for real in-cylinder ressure cycle analysis in internal combustion engines. Energy 2011, 36, [CrossRef] 29. Payri, F.; Luján, J.M.; Martín, J.; Abbad, A. Digital signal rocessing of in-cylinder ressure for combustion diagnosis of internal combustion engines. Mech. Syst. Signal Process. 2010, 24, [CrossRef] 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an oen access article distributed under the terms and conditions of the Creative Commons Attribution CC BY license htt://creativecommons.org/licenses/by/4.0/.