An apparatus and a method for determining an efficiency index of a process involving a use of a mechanical system

Abstract

An apparatus for determining an efficiency index of a process comprises processing equipment (103) for receiving data indicative of service produced by the process and data indicative of efficiency parameters needed for production of the service The apparatus comprises a memory (101) storing response quantities each associated with a predetermined stress range and expressing an upper limit for number of stress cycles at an observation point of a mechanical system used in the process, where the stress cycles have the stress range related to the response value. The processing equipment updates stress history quantities expressing number of occurred stress cycles having stress ranges related to the response quantities. A fatigue damage sum is estimated based on the response quantities and the stress history quantities. The efficiency index is formed based on the service, the efficiency parameters, and the fatigue damage sum.

Description

[0001] An apparatus and a method for determining an efficiency index of a process involving a use of a mechanical system

[0002] Field of technology

[0003] The disclosure relates generally to obtaining data for controlling and / or optimizing processes involving a use of a mechanical system. More particularly, the disclosure relates to an apparatus and to a method for determining an efficiency index of a process involving a use of a mechanical system, where the efficiency index constitutes at least a part of data for controlling and / or optimizing the process. Furthermore, the disclosure relates to a computer program for determining an efficiency index of a process involving a use of a mechanical system.

[0004] Background

[0005] In many cases, there is a desire to control and / or optimize a process so that a produced service is maximized with respect to used efficiency parameters or, alternatively, the use of the efficiency parameters is minimized with respect to the produced service. The process can be for example a manufacturing or production process where produced products represent the produced service and where the efficiency parameters can be for example consumption of raw materials, consumption of energy, consumption of time, production of waste, and emission of unwanted substances such as e.g. carbon dioxide CO2. For another example, the process can be a transport service where a transport performance, expressed e.g. in person-kilometers or in ton-kilometers, represents the produced service and where the efficiency parameters can be for example consumption of energy, consumption of time, and emission of unwanted substances such as carbon dioxide CO2. Many approaches have been taken to control and optimize processes of the kind mentioned above. Examples of these approaches include the Lean Six Sigma’s Define, Measure, Analyze, Improve and Control “DMAIC”, the Business Process Reengineering “BPR”, and the Results-Root Causes-Remediation-Rhythm “4R” methodology. A process of the kind mentioned above comprises typically a use of a mechanical system that can be for example of a production machinery, a transportation device such as a vehicle, or a working machine such as a crane or an excavator. The mechanical system comprises often mechanical structures which are subjected to cyclic mechanical loading which may cause fatigue in materials of the mechanical structures. If the above-mentioned cyclic mechanical loading is above a certain threshold, microscopic cracks will begin to form at stress concentrators such as for example surfaces, persistent slip bands “PSB”, interfaces of constituents in a case of composites, and grain interfaces in a case of metals. After crack initiation, the crack will propagate, and eventually the mechanical structure will finally fracture. The shape of the mechanical structure will significantly affect the fatigue strength. For example, square holes and sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Instead, round holes and smooth transitions and fillets will increase the fatigue strength of the mechanical structure. In welded metal structures, areas adjacent to welded joints are often critical since a local geometry and existence of high residual stress and welding deformations in welded joints are often suboptimal from the viewpoint of the fatigue strength.

[0006] An inherent challenge related to damages caused by material fatigue is that the above-mentioned microscopic cracks are typically not recognized during a use of a mechanical structure. A further challenge is that the crack propagation will accelerate in accordance with an increasing crack length and therefore the mechanical structure may fracture even if the loading remains unchanged. Thus, in many cases, fatigue in materials of mechanical structures may cause expensive and surprising interruptions of a process for producing a desired service, and thereby the control and / or optimization of the process may deteriorate or even fail.

[0007] Summary

[0008] The following presents a simplified summary to provide a basic understanding of some aspects of various invention embodiments. The summary is not an extensive overview of the invention. It is neither intended to identify key or critical elements of the invention nor to delineate the scope of the invention. The following summary merely presents some concepts of the invention in a simplified form as a prelude to a more detailed description of exemplifying embodiments of the invention.

[0009] In accordance with the present invention, there is provided a new apparatus for determining an efficiency index of a process that involves a use of a mechanical system that can be for example of a production machinery, a transportation device such as a vehicle, or a working machine such as a crane or an excavator. The efficiency index is indicative of production of service by the process with respect to usage of one or more efficiency parameters needed for production of the service. Thus, the efficiency index constitutes at least a part of data suitable for controlling and / or optimizing the process.

[0010] The apparatus according to the invention comprises:

[0011] - processing equipment configured to receive first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service, and,

[0012] - memory equipment storing a database containing predetermined response quantities each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system, wherein the processing equipment is configured to:

[0013] - repeatedly update, for each of the response quantities, a corresponding stress history quantity expressing number of stress cycles occurred in a timetrend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration, - repeatedly update a fatigue damage sum based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and

[0014] - form the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum as an additional efficiency parameter.

[0015] The fatigue damage sum expresses a cumulated fatigue damage of the mechanical system, and therefore the fatigue damage sum can be used for real-time fatigue monitoring during a lifetime of the mechanical system. As the fatigue damage sum is used as an additional efficiency parameter when forming the efficiency index, material fatigue development of the mechanical system is taken into account when the process is controlled and / or optimized based on the efficiency index.

[0016] It is worth noting that computations carried out for updating the above-mentioned fatigue damage sum are not necessarily carried out with stress values, but as well the computations can be carried out with values of another quantity, such as cyclic loading, strain, loading forces, acceleration, displacements, etc., related directly or indirectly to the stress. For example, each response quantity can be associated with one of predetermined strain ranges. The response quantity is however indirectly associated with one of predetermined stress ranges because the strain is related to the stress via a deterministic rule.

[0017] In accordance with the present invention, there is provided also a new method for determining an efficiency index of a process that involves a use of a mechanical system. The method comprises:

[0018] - receiving first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service, maintaining a database containing predetermined response quantities each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system,

[0019] - repeatedly updating, for each of the response quantities, a corresponding stress history quantity expressing number of stress cycles occurred in a timetrend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration,

[0020] - repeatedly updating a fatigue damage sum based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and

[0021] - forming the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum as an additional efficiency parameter.

[0022] In accordance with the invention, there is provided also a new computer program for determining an efficiency index of a process that involves a use of a mechanical system. The computer program comprises computer executable instructions for controlling programmable processing equipment to:

[0023] - receive first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service,

[0024] - maintain a database containing predetermined response quantities each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system, - repeatedly update, for each of the response quantities, a corresponding stress history quantity expressing number of stress cycles occurred in a timetrend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration,

[0025] - repeatedly update a fatigue damage sum based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and

[0026] - form the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum as an additional efficiency parameter.

[0027] In accordance with the invention, there is provided also a new computer program product. The computer program product comprises a non-volatile computer readable medium, e.g. a compact disc “CD”, encoded with a computer program according to the invention.

[0028] Various exemplifying and non-limiting embodiments are described in accompanied dependent claims.

[0029] Exemplifying and non-limiting embodiments both as to constructions and to methods of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific exemplifying embodiments when read in conjunction with the accompanying drawings.

[0030] The verbs “to comprise” and “to include” are used in this document as open limitations that neither exclude nor require the existence of also un-recited features.

[0031] The features recited in the accompanied dependent claims are mutually freely combinable unless otherwise explicitly stated.

[0032] Furthermore, it is to be understood that the use of “a” or “an”, i.e. a singular form, throughout this document does not exclude a plurality. Brief description of the figures

[0033] Exemplifying and non-limiting embodiments and their advantages are explained in greater detail below in the sense of examples and with reference to the accompanying drawings, in which: figure 1 a illustrates a mechanical system and an apparatus according to an exemplifying and non-limiting embodiment for determining an efficiency index of a process involving a use of the mechanical system, and figure 1 b shows a part of the mechanical system and a functional block diagram of the apparatus, figure 2 shows a functional block diagram of an apparatus according to another exemplifying and non-limiting embodiment for determining an efficiency index of a process involving a use of a mechanical system, and figure 3 shows a flowchart of a method according to an exemplifying and non-limiting embodiment for determining an efficiency index of a process involving a use of a mechanical system.

[0034] Description of exemplifying and non-limiting embodiments

[0035] The specific examples provided in the description below should not be construed as limiting the scope and / or the applicability of the accompanied claims. Lists and groups of examples provided in the description are not exhaustive unless otherwise explicitly stated.

[0036] Figure 1 a illustrates a mechanical system 108 and an apparatus 100 according to an exemplifying and non-limiting embodiment for determining an efficiency index r| of a process involving a use of the mechanical system 108. In this exemplifying case, the mechanical system 108 comprises a crane for lifting and transferring loads. The process can be for example a loading and / or unloading process of transport devices such as ships, trucks, or railway carriages. A control system 106 is configured to gather data from the process and to control and / or optimize the process based on control data including the above-mentioned efficiency index r|. It is to be noted that the mechanical system 108 is shown for illustrative purposes only, and the apparatus 100 is applicable with many different processes and mechanical systems.

[0037] Figure 1 b shows a functional block diagram of the apparatus 100 and a mechanical structure 109 that is a part of the mechanical system 108. In the exemplifying situation shown in figure 1 b, the mechanical structure 109 comprises a welded joint 110. Material fatigue at an observation point 111 of the mechanical structure 109 is monitored. The mechanical system 108 may have one or more other observation points and material fatigue at each of the one or more other observation points can be monitored in the same way as the material fatigue is monitored at the observation point 111.

[0038] The apparatus 100 comprises processing equipment 103 configured to receive first data indicative of service S produced by the process and second data indicative of one or more efficiency parameters Ci, C2, ... , Cnneeded for production of the service S. In the exemplifying case illustrated in figure 1a, the first and second data are received from the control system 106. The service S produced by the process can be for example a cumulative mass or a cumulative number of pieces loaded and / or unloaded by the mechanical system 108. The one or more efficiency parameters Ci , C2, ... , Cnmay express for example energy and / or other resources consumed by the process and / or emissions, e.g. CO2 emissions, produced by the process and / or other environmental loads such as noise, heat, mechanical vibrations, mechanical impacts, light pollution, dust, etc. caused by the process. Furthermore, one or more of the efficiency parameters can be one or more fixed efficiency parameters needed for production of the service S. The fixed efficiency parameters may express for example material needed for constructing the mechanical system 108 and possible other elements needed in the process, energy needed for constructing the mechanical system 108 and the possible other elements, emissions of unwanted substances such as CO2 created when constructing the mechanical system 108 and the possible other elements, and / or other environmental loads caused when constructing the mechanical system 108 and the possible other elements. The fixed efficiency parameters of the kind mentioned above do not represent efficiency parameters used by the process but, nevertheless, the fixed efficiency parameters of the kind mentioned above are efficiency parameters needed for production of the service.

[0039] In many cases, the service S can be expressed for example in terms of money, e.g. in euros or US dollars and, correspondingly, the one or more efficiency parameters Ci, C2, ... , Cncan be expressed for example as cost factors in terms of money, e.g. in euros or US dollars, because the prices or economical values of the service and the efficiency parameters may be known, e.g. a price of a service unit, a price of energy, and a price of an emitted ton of CO2 are often known. In many cases, the price or economical value of efficiency parameters which are used during the process can be deemed to be operating expenses “OPEX” whereas fixed efficiency parameters of the kind mentioned above can be deemed to be capital expenses “CAPEX”.

[0040] The apparatus 100 comprises memory equipment 101 storing a database 102 that contains predetermined response quantities R1, ... , RQ each being associated with one of predetermined stress ranges Am, Am, AGQ SO that each of the response quantities R1, ... , RQ expresses an upper limit for number of stress cycles at the predetermined observation point 111 in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration. The upper limit corresponds to a predetermined survival probability of the mechanical structure 109 in the above-described situation.

[0041] In this exemplifying embodiment, each of the predetermined response quantities R1, ... , RQ is a scalar quantity that can be estimated based on the fatigue performance of the mechanical structure 109. In general, the stress should not exceed the yield strength of material under consideration. In an exemplifying case where a thin and slender mechanical structure is under monitoring, the maximum allowable compressive stress related to the buckling capacities, such as plate buckling, flexural, or lateral buckling of columns, should not be exceeded.

[0042] Each response quantity Rq, where q = 1 , 2, ... , Q can be computed for example according to the following equation: where Cref is a fatigue performance that is specific to the mechanical structure under consideration and corresponds to a selected survival probability, Aoqis the stress range at the observation point of the mechanical structure, and mref is a model parameter i.e. the slope of the S-N curve e.g. 5.85. Riocaiis a local stress ratio at the observation point of the mechanical structure: r> >ffmean_Acr / 2

[0043] Klocal - ~ ff,A„ / 9> (2) mean+ Acr / 2 where Gmean and AG are the mean stress and the stress range, respectively, at the observation point of the mechanical structure, considering the material elastoplastic behavior.

[0044] The above-mentioned local stress ratio Riocaiand subsequently the response quantity Rqdepend on, among others, material strength, residual stresses within the mechanical structure both in as-welded or post treated conditions, geometry and dimensions of the mechanical structure, welded joint and / or cut edge parameters, such as e.g. weld toe or root side geometry for a welded joint and surface quality for a cut edge.

[0045] Theoretical background related to the above-presented equations 1 and 2 can be found in the publication: Timo Nykanen and Timo Bjork: Assessment of fatigue strength of steel buttwelded joints in as-welded condition - Alternative approaches for curve fitting and mean stress effect analysis, Lappeenranta University of Technology, Laboratory of Steel Structures, Marine Structures 44, 2015, pp. 288 - 310, Elsevier Ltd, and in the publication: Timo Nykanen and Timo Bjork: A new proposal for assessment of the fatigue strength of steel buttwelded joints improved by peening under constant amplitude tensile loading, School of Energy Systems, Lappeenranta University of Technology, Wiley Publishing Ltd. Fatigue Fract Engng Mater Struct, 2016, 39, pp. 566-582. It is to be however noted that the above- mentioned response quantities Ri, ... , RQ can be obtained with any suitable method, and therefore the invention is not limited to any particular method for obtaining the response quantities Ri, RQ.

[0046] The processing equipment 103 is configured to repeatedly update, for each of the above-mentioned response quantities Ri, RQ, a corresponding stress history quantity hi(t), ... , ho(t). In this exemplifying embodiment, each of the stress history quantities hi (t), ... , ho(t) is a scalar quantity that expresses number of stress cycles which have occurred in the time-trend of the stress o(t) and which have the predetermined stress range related to the corresponding response quantity. The stress history quantities hi (t), ... , ho(t) are presented as functions of time t because their values develop along with the time. The update rate can be e.g. in the range from 0.01 Hz to 20 Hz. In other words, a time interval between successive updates of the stress history quantities hi(t), ... , ho(t) can be from 50 millisecond to 100 seconds. In the exemplifying apparatus illustrated in figure 1 b, the memory equipment 101 stores a database 107 that contains the stress history quantities hi(t), ... , hQ(t).

[0047] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to run the Rainflow-counting algorithm to update the stress history quantities hi(t), ... , ho(t) based on the time-trend of the stress cr(t) at the observation point 111 of the mechanical structure 109. The Rainflow-counting algorithm, also known as the “Rain-flow counting method”, is commonly used in fatigue analyses and monitoring to reduce a spectrum of timevarying stress into a set of cycle counts corresponding to a given set of stress variation ranges. More detailed information about the Rainflow-counting algorithm can be found e.g. in the publication M. Matsuishi and T. Endo: Fatigue of metals subjected to varying stress, Japan Society of Mechanical Engineering 1968. It is to be however noted that there are many cycle-counting algorithms for fatigue analyses and monitoring, and therefore the invention is not limited to any specific cycle-counting algorithm.

[0048] The processing equipment 103 is configured to repeatedly update a fatigue damage sum D based on the response quantities Ri, ... , RQ and on the stress history quantities hi (t), ... , ho(t) related to the response quantities. The fatigue damage sum D expresses cumulated fatigue damage of the mechanical structure 109 and it can be used for estimating a remaining service producible by the mechanical structure 108. The update rate can be e.g. in the range from 0.01 Hz to 20 Hz. In other words, a time interval between successive updates of the fatigue damage sum D can be from 50 millisecond to 100 seconds.

[0049] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the fatigue damage sum D according to the Palmgren-Miner damage accumulation formula:

[0050] The processing equipment 103 is configured to form the efficiency index r| based on the service S produced by the process, the one or more efficiency parameters Ci , C2, ... , Cn, and the fatigue damage sum D.

[0051] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the efficiency index r| according to the following formula: where S and Ci , C2, ... , Cn, are the service and the efficiency parameters cumulated over the whole time when the process has been used or over a given measurement time-period, and a is a constant.

[0052] In an exemplifying and non-limiting embodiment, the efficiency index r| is computed according to the following formula: where kmis a factor expressing amount of material needed when constructing the mechanical system 108 and possible other elements needed in the process, kco2 is a coefficient expressing disadvantage, e.g. costs, per a unit of emitted CO2, eoco2 is the CO2 emission caused when constructing the mechanical system 108 and possible other elements needed in the process, eco2 is the CO2 emission caused by the process when producing the service S, Eo is energy needed when constructing the mechanical system 108 and possible other elements needed in the process, kEo is a coefficient expressing disadvantage, e.g. pollution, per a unit of the energy Eo, E is energy consumed by the process when producing the service S, and KE is a coefficient expressing disadvantage, e.g. pollution, per a unit of the energy E. In this exemplifying case, one of the efficiency parameters is the weighted sum KEO EO + KE E which relates to both the energy needed for the construction of the mechanical system and possible other elements and the energy needed by the process to produce the service S. Another one of the efficiency parameters is the sum eoco2 + eoco2 which relates to both the CO2 emission caused when the constructing of the mechanical system and the possible other elements and the CO2 emission caused when producing the service S. The term eoco2 can be indicative of differences between for example fossil-freely produced steel and conventionally produced steel, and this term eoco2 may be significant when looking for optimal applications for fossil-freely produced steel.

[0053] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute an estimate for a production rate dS / dt of the service S, and to compute one or more estimates for one or more usage rates dCi / dt, dC2 / dt, ... , dCn / dt of the one or more efficiency parameters Ci , C2, ... , Cn. Furthermore, the processing equipment 103 is configured to compute an estimate for a growth rate dD / dt of the fatigue damage sum. The growth rate can estimated for example as (D(to) - D(t-i )) / (to - 1-1), where to is an update moment of the fatigue damage sum D and correspondingly t-1 is an earlier update moment of the fatigue damage sum D. Numerical derivation of the kind mentioned above is however susceptible to disturbances, and thus it can be more advantageous to fit a polynomial or some other suitable curve with the time-discrete values of the fatigue damage sum D and thereafter to estimate the instantaneous growth rate with the derivative of the polynomial or the other suitable curve. Correspondingly, the estimate for the production rate dS / dt and the estimates for the usage rates dCi / dt, dC2 / dt, ... , dCn / dt can be formed in the above-mentioned way. In this exemplifying and non-limiting embodiment, the processing equipment 103 is configured to form the efficiency index r| based on the estimate of the production rate dS / dt of the service, the one or more estimates of the one or more usage rates dCi / dt, dC2 / dt, ... , dCn / dt of the efficiency parameters, and the estimate of the growth rate dD / dt of the fatigue damage sum.

[0054] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the efficiency index r| according to the following formula:

[0055] In an exemplifying and non-limiting embodiment, the efficiency index r| is computed according to the following formula: where y is a constant. Formula 7 is factually a scaled product of n+1 efficiency indices r|ixr|2x...xr|nxy, where r|i = (dS / dt) / (dCi / dt), r|2 = (dS / dt) / (dC2 / dt), r|n= (dS / dt) / (dCn / dt), and r|D = (dS / dt) / (dD / dt).

[0056] In an exemplifying and non-limiting embodiment, the efficiency index r| is computed according to the following formula:

[0057] The parameters and variables in formula 8 have been explained above in conjunction with formula 5. Formula 5 describes the efficiency index in the light of a cumulative situation taking into account not only the process but also the construction of the mechanical system and possible other elements needed in the process. Instead, formula 8 describes a momentary situation expressing an increment of the service obtained with increments of usage of the efficiency parameters. Therefore, formula 8 is advantageous for online control of the process.

[0058] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the efficiency index r| according to the following formula: dt dt nom dt dt nom dt dt nom dt dtnOm where dS / dtnom is a nominal value of the production rate, dCi / dtnOm, dC2 / dtnOm, ... , dCn / dtnom are nominal values of the usage rates of the efficiency parameters, and dD / dtnom is a nominal value of the growth rate of the fatigue damage sum, and 6 is a constant.

[0059] As illustrated by the above-presented examples, there are many ways to define the efficiency index r| so that the fatigue damage sum is used as an additional efficiency parameter. A suitable way to define the efficiency index r| depends on a process and / or a mechanical system under consideration. Therefore, the invention is not limited to any specific ways to define the efficiency index.

[0060] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 shown in figure 1 b is configured to repeatedly estimate the stress o(t) at the observation point 111 of the mechanical structure 109 based on data indicative of mechanical loading directed to the mechanical structure 109. The estimating rate can be e.g. in the range from 0.01 Hz to 20 Hz. In other words, a time interval between successive estimates of the stress o(t) can be from 50 millisecond to 100 seconds. The measuring rate is advantageously significantly greater than the above-mentioned estimating rate. The measuring rate can be for example in the range from 1 Hz to 5 kHz. It is also possible that the apparatus comprises a data interface for receiving, from an external device, data indicative of the stress o(t) at the observation point 111 of the mechanical structure 109. In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the stress o(t) at the observation point 111 as a weighted sum of i) membrane stress om(t) and ii) bending stress crb(t) acting on an area of the mechanical structure 109 a distance away from the observation point 111 of the mechanical structure 109. The weight factors of the weighted sum are predetermined local stress concentration factors Kt,mand Kt,b defined separately for the membrane and bending stresses om(t) and ob(t). Therefore, in this exemplifying case, the processing equipment 103 is configured to compute the stress o(t) according to the following equation: o(t) = Kt.rn Om(t) + Kt,b Ob(t). (10)

[0061] An exemplifying way to determine the local stress concentration factors based on the finite element analysis “FEA” is presented in the publication A. Ahola, T. Nykanen and T. Bjork: Effect of loading type on the fatigue strength of asymmetric and symmetric transverse non-load carrying attachments, School of Energy Systems, Lappeenranta University of Technology, Wiley Publishing Ltd. Fatigue Fract Engng Mater Struct, 2017, 40, pp. 670-682. An exemplifying way to determine the local stress concentration factors based on an artificial neutral network “ANN” is presented in the publication M. Dabiri, M. Ghafouri, H. R. Rohani Raftar, and T. Bjork: Neural network-based assessment of the stress concentration factor in a T- welded joint, Laboratory of Steel Structures, Lappeenranta University of Technology, Journal of Constructional Steel Research 128, 2017, pp. 567-578. An exemplifying way to determine the local stress concentration factors based on analytical equations is presented in the publication K. lida and T. Uemura: Stress concentration factor formulae widely used in Japan, University of Tokyo, Fatigue Fract. Engng Mater. Struct. Vol. 19, No. 6, pp. 779-786, 1996.

[0062] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the above-mentioned membrane stress om(t) and the bending stress ob(t) based on outputs s1 (t) and s2(t) of strain gauges 104 and 105 attached to the mechanical structure 109. The membrane stress om(t) is proportional to an average (s1 (t) + s2(t)) / 2 of the outputs of the strain gauges 104 and 105, and the bending stress ob(t) is proportional to a difference s1 (t) - s2(t) of the outputs of the strain gauges 104 and 105. In many cases, there can be more than two strain gauges.

[0063] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 103 is configured to compute the stress o(t) at the observation point 111 of the mechanical structure 109 based on forces directed to the mechanical structure 109, on an inverse of a stiffness matrix of a finite element model “FEM” of at least a part of the mechanical structure 109, and on element level force-displacement equations of the finite element model expressing the stress ok(t) as a function of nodal displacements of appropriate nodes of the finite element model. In an exemplifying case where the mechanical structure 109 operates in the linear area so that the Hooke’s law is valid, the memory equipment 101 is advantageously configured to store the inverse of the stiffness matrix of the finite element model and the processing equipment 103 is advantageously configured to use the stored inverse of the stiffness matrix when repeatedly computing the stress cr(t). Thus, there is no need to compute the inverse of the stiffness matrix every time when the stress o(t) is computed.

[0064] If the computational performance of the processing equipment 103 is sufficient with respect to complexity of data processing operations to be carried out by the processing equipment 103, the efficiency index can be determined in real time and the process can be controlled with the real-time efficiency index. For example, the complexity of data processing operations is rather low in the above-described case based on the above-mentioned equation 10 and the above-mentioned strain gauges, and thus real time operation is achievable. The complexity of data processing operations is significantly higher in the above-described case based on the finite element model and thus a greater computational performance is needed for real time operation.

[0065] An apparatus according to an exemplifying and non-limiting embodiment can be used for determining the efficiency index in a simulated case where the mechanical system 108 and possible other elements needed for the process are modelled with simulation models and the process is simulated with the aid of these simulation models. Appropriate parts of the mechanical system 108 and possible other elements can be modelled with e.g. the finite element model “FEM”. Furthermore, efficiency parameters, e.g. CO2 emissions, material needs, etc., related to construction of the mechanical system 108 and possible other elements needed for the process can be based on simulations, and these simulated efficiency parameters can be involved in the determination of the efficiency index based on the simulated process. An inherent advantage of the simulations is that different alternatives with different boundary conditions can be compared to each other even if no real system has not been constructed yet. When comparing the different alternatives to each other, it may be advantages to express the service in terms of money and the efficiency parameters as cost factors in terms of money to find out an economical optimum. The processing equipment 103 can be configured to run the simulation of the process with the aid of the simulation models, or there can be another processing system for running the simulation of the process with the aid of the simulation models. In the later mentioned case, the processing equipment 103 can receive the data indicating the service, the efficiency parameters, and possible other quantities from the other processing system in a same way as from a real system. The efficiency parameters related to construction of the mechanical system 108 and possible other elements needed for the process can be simulated off-line prior to simulating the process for producing the service.

[0066] If the computational performance of the processing equipment 103 and the possible other processing system is sufficient with respect to complexity of data processing operations to be carried out, the simulated process can run in real time in parallel with the real process in the real system, and the efficiency index can be determined in real time and the real process can be controlled with the real-time efficiency index. If the computational performance is high, it is even possible that the simulated time runs faster than the real time. This is advantageous when many different alternatives with many different boundary conditions are compared to each to find out an optimum. Fast simulations are naturally advantageous when a lot of simulations are to be done, e.g. when an optimum is searched by using a genetic algorithm or the like.

[0067] In an apparatus according to an exemplifying and non-limiting embodiment, each of the response quantities R1, ... , RQ is associated, in addition to the predetermined stress range, with one or more quantities descriptive of operating conditions of the mechanical structure 109. The one or more quantities may comprise for example temperature of the mechanical structure 109 because the strength capacity of the mechanical structure 109 may depend on the temperature. In this exemplifying case, the processing equipment 103 is configured to update each stress history quantity hi (t), ... , ho(t) to express number of cycles occurred in the time-trend of the stress so that 1 ) the occurred cycles have the predetermined stress range related to the corresponding response quantity and 2) the operating conditions of the mechanical structure 109 correspond to the one or more quantities related to the response quantity under consideration, e.g. the temperature of the mechanical structure belongs to a temperature range related to the response quantity under consideration and / or an effect of a corrosive environment on the material fatigue corresponds to a same effect of a corrosive environment related to the response quantity under consideration. In this exemplifying embodiment, one or more of the response quantities Ri, ... , RQ can be related to a same stress range, and the one or more quantities descriptive of the operating conditions make difference between these response values.

[0068] Figure 2 shows a functional block diagram of an apparatus according to an exemplifying and non-limiting embodiment for determining an efficiency index r| of a process involving a use of the mechanical system 108 shown in figure 1 a. Figure 2 shows the mechanical structure 109 that constitutes a part of the mechanical system 108. The apparatus comprises processing equipment 203 configured to receive first data indicative of service S produced by the process and second data indicative of one or more efficiency parameters Ci , C2, ... , Cnneeded for production of the service S. In the exemplifying case illustrated in figure 2, the first and second data are received from the control system 106.

[0069] In this exemplifying and non-limiting embodiment, each of the response quantities R1, ... , RQ is a vector of response values Ni,i, ... , NP,Q each of which is associated with one of predetermined stress ranges Am, Am, ... , . AOQ and one of predetermined mean stresses 01, mean,... , op, mean so that each of the response values Ni,i, ... , NP,Q expresses an upper limit for number of stress cycles at the predetermined observation point 111 in a situation in which stress cycles have the predetermined stress range Ac and the predetermined mean stress Gmean related to the response value under consideration. The upper limit corresponds to a predetermined survival probability of the mechanical structure 109 in the abovedescribed situation. Each of the predetermined response values Ni,i, ... , NP,Q can be estimated based on the fatigue performance of the mechanical structure 109. The apparatus comprises memory equipment 201 storing a database 202 that contains the above-mentioned response values Ni,i, ... , NP,Q. Correspondingly, each of the stress history quantities hi (t), ... , ho(t) is a vector of stress history values m,i(t), ... , np,Q(t).

[0070] Each response value Nk,q, where k = 1 , 2, ... , P and q = 1 , 2, ... , Q can be computed for example according to the above-presented equations 1 and 2 so that not only the stress range Ac in equation 1 is varied but also the mean stress Gmean in equation 2 is varied and thus the response values Ni ,1 , ... , NP,Q can be arranged to constitute a two-dimensional array as illustrated in figure 2 so that one dimension corresponds to the stress range whereas the other dimension corresponds to the mean stress. It is to be however noted that the response values Ni,i, ... , NP,Q can be obtained with any suitable method, and therefore the invention is not limited to any particular method for obtaining the response values Ni ,1 , ... , NP,Q.

[0071] The apparatus comprises processing equipment 203 configured to repeatedly update, for each of the above-mentioned response values Ni,i, ... , NP,Q, the corresponding stress history value ni,i(t), ... , np,o(t) that expresses number of cycles which have occurred in the time-trend of the stress o(t) and which have the predetermined stress range and the predetermined mean stress related to the corresponding response value. The stress history values ni,i(t), ... , np,o(t) are presented as functions of time t because their values develop along with the time. The update rate can be e.g. in the range from 0.01 Hz to 20 Hz. In other words, a time interval between successive updates of the stress history values ni,i(t), ... , np,o(t) can be from 50 millisecond to 100 seconds. In the exemplifying apparatus illustrated in figure 2, the memory equipment 201 stores a database 207 that contains the stress history values ni,i(t), ... , np,o(t). In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to run the Rainflow-counting algorithm to update the stress history values ni,i(t), np,o(t) based on the time-trend of the stress cr(t) at the observation point 111 of the mechanical structure 109. The Rainflow-counting algorithm is an example of suitable methods for reducing a timevarying stress into a set of cycle counts corresponding to a given set of mean values and a given set of stress variation ranges. It is to be however noted that there are many cycle-counting algorithms for the above-mentioned task, and therefore the invention is not limited to any specific cycle-counting algorithm.

[0072] The processing equipment 103 is configured to repeatedly update a fatigue damage sum D based on the response values Ni,i, ... , NP,Q and the corresponding stress history values ni,i(t), ... , np,o(t) related to the response values. The update rate can be e.g. in the range from 0.01 Hz to 20 Hz. In other words, a time interval between successive updates of the fatigue damage sum D can be from 50 millisecond to 100 seconds.

[0073] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to compute the fatigue damage sum D according to the Palmgren-Miner damage accumulation formula:

[0074] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to form the efficiency index based on the service S produced by the process, the one or more efficiency parameters Ci , C2, ... , Cn, and the fatigue damage sum D. In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to compute the efficiency index r| according to the above-presented formula 4 or formula 5.

[0075] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to compute an estimate for a production rate dS / dt of the service S, compute one or more estimates for one or more usage rates dCi / dt, dC2 / dt, dCn / dt of the one or more efficiency parameters Ci, C2, Cn, and compute an estimate for a growth rate dD / dt of the fatigue damage sum. The processing equipment 203 is configured to form the efficiency index r| based on the estimate of the production rate dS / dt of the service, the one or more estimates of the one or more usage rates dCi / dt, dC2 / dt, dCn / dt of the efficiency parameters, and the estimate of the growth rate dD / dt of the fatigue damage sum.

[0076] In an apparatus according to an exemplifying and non-limiting embodiment, the processing equipment 203 is configured to compute the efficiency index r| according to the above-presented formula 6, formula 7, formula 8, or formula 9.

[0077] In an apparatus according to an exemplifying and non-limiting embodiment, each of the response values Ni,i, ... , NP,Q is associated, in addition to the predetermined stress range and the predetermined mean stress, with one or more quantities descriptive of operating conditions of the mechanical structure 109. The one or more quantities may comprise for example temperature of the mechanical structure 109 because the strength capacity of the mechanical structure 109 may depend on the temperature. In this exemplifying case, the processing equipment 203 is configured to update each stress history value ni,i(t), ... , np,o(t) to express number of cycles occurred in the time-trend of the stress so that 1 ) the occurred cycles have the predetermined stress range and the predetermined mean stress related to the corresponding response value and 2) the operating conditions of the mechanical structure 109 correspond to the one or more quantities related to the response value under consideration, e.g. the temperature of the mechanical structure belongs to a temperature range related to the response value under consideration and / or an effect of a corrosive environment on the material fatigue performance corresponds to a same effect of a corrosive environment related to the response value under consideration. In this exemplifying embodiment, one or more of the response values N1 ,1 , ... , NP,Q can be related to a same stress range and to a same mean stress, and the one or more quantities descriptive of the operating conditions make difference between these response values.

[0078] The implementation of the processing equipment 103 shown in figure 1 a and 1 b as well as the implementation of the processing equipment 203 shown in figure 2 can be based on one or more analogue circuits, one or more digital processing circuits, or a combination thereof. Each digital processing circuit can be a programmable processor circuit provided with appropriate software, a dedicated hardware processor such as for example an application specific integrated circuit “ASIC”, or a configurable hardware processor such as for example a field programmable gate array “FPGA”. The memory equipment 101 shown in figure 1 a and 1 b as well as the memory equipment 201 shown in figure 2 may comprise one or more memory circuits each of which can be for example a Random-Access Memory “RAM” circuit.

[0079] Figure 3 shows a flowchart of a method according to an exemplifying and nonlimiting embodiment for determining an efficiency index of a process that involves a use of a mechanical system. The method comprises the following actions:

[0080] - action 301 : receiving first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service,

[0081] - action 302: maintaining a database containing predetermined response quantities each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system,

[0082] - action 303: repeatedly updating, for each of the response quantities, a corresponding stress history quantity expressing number of stress cycles occurred in a time-trend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration, action 304: repeatedly updating a fatigue damage sum based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and

[0083] - action 305: forming the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum as an additional efficiency parameter.

[0084] The first data can be indicative of for example one or more of the following: number of produced products, mass of produced product, economical value of produced product or products, a transport service in person-kilometers, and a transport service in ton-kilometers.

[0085] The second data can be indicative of for example one or more of the following efficiency parameters: energy consumed by the process, emissions such as CO2 emissions produced by the process, amount of waste produced by the process, and amount of raw materials consumed by the process.

[0086] A method according to an exemplifying and non-limiting embodiment comprises computing the efficiency index r| according to the formula: where Ci, C2, ... , and Cnare the efficiency parameters, S is the service, D is the fatigue damage sum, and a is a constant.

[0087] A method according to an exemplifying and non-limiting embodiment comprises computing an estimate for a production rate dS / dt of the service, computing one or more estimates for one or more usage rates dCi / dt, dC2 / dt, ... , dCn / dt of the one or more efficiency parameters Ci , C2, ... , and Cn, computing an estimate for a growth rate dD / dt of the fatigue damage sum, and forming the efficiency index r| based on the estimates of the production rate of the service, the one or more usage rates of the efficiency parameters, and the growth rate of the fatigue damage sum.

[0088] A method according to an exemplifying and non-limiting embodiment comprises computing the efficiency index r| according to the formula: where dCi / dt, dC2 / dt, ... and dCn / dt are the estimates of the usage rates of the efficiency parameters Ci , C2, ... and Cn, dS / dt is the estimate of the production rate of the service, dD / dt is the estimate of the growth rate of the fatigue damage sum, and p is a constant.

[0089] In a method according to an exemplifying and non-limiting embodiment, each of the response quantities is a vector of response values so that each of the response values is associated with the predetermined stress range related to the response quantity and to one of predetermined mean stresses, and each of the response values expresses an upper limit for number of cycles of stress at the predetermined observation point of the mechanical system in a situation in which the cycles have the predetermined stress range related to the response quantity and the predetermined mean stress related to the response value under consideration. Correspondingly, each of the stress history quantities is a vector of stress history values, and the method comprises repeatedly updating, for each of the response values, the corresponding stress history value expressing number of cycles occurred in the time-trend of the stress and having the predetermined stress range and the predetermined mean stress related to the response value under consideration, and repeatedly updating the fatigue damage sum based on the response values and the stress history values related to the response values.

[0090] A method according to an exemplifying and non-limiting embodiment comprises computing the fatigue damage sum D according to the formula:

[0091] D =y , N'Jwhere nij (t) is the stress history value expressing the number of the cycles occurred in the time-trend of the stress and having the ithpredetermined stress range and the jthpredetermined mean stress, and Ni is the response value relating to the ithpredetermined stress range and to the jthpredetermined mean stress. A method according to an exemplifying and non-limiting embodiment comprises repeatedly estimating the stress at the predetermined observation point of the mechanical system based on data indicative of mechanical loading directed to the mechanical system.

[0092] A method according to an exemplifying and non-limiting embodiment comprises computing the stress as a weighted sum of i) membrane stress and ii) bending stress acting on an area of the mechanical system a distance away from the predetermined observation point of the mechanical system. The weight factors of the weighted sum are predetermined local stress concentration factors defined separately for the membrane and bending stresses.

[0093] A method according to an exemplifying and non-limiting embodiment comprises computing the membrane stress and the bending stress based on outputs of strain gauges attached to the mechanical system. The membrane stress is proportional to an average of the outputs of the strain gauges and the bending stress is proportional to a difference of the outputs of the strain gauges.

[0094] A method according to an exemplifying and non-limiting embodiment comprises computing the stress based on forces directed to the mechanical system, an inverse of a stiffness matrix of a finite element model of at least a part of the mechanical system, and element level force-displacement equations of the finite element model expressing the stress as a function of nodal displacements of the finite element model.

[0095] A method according to an exemplifying and non-limiting embodiment comprises storing the inverse of the stiffness matrix of the finite element model in memory equipment and using the stored inverse of the stiffness matrix when repeatedly computing the stress.

[0096] In a method according to an exemplifying and non-limiting embodiment, each of the response quantities is associated, in addition to the predetermined stress range, with one or more condition quantities descriptive of operating conditions of the mechanical system e.g. temperature at the predetermined observation point of the mechanical system. In the method according to this exemplifying and non-limiting embodiment, each stress history quantity is updated to express number of cycles occurred in the time-trend of the stress so that 1 ) the occurred cycles have the predetermined stress range related to the response quantity under consideration and 2) the operating conditions of the mechanical system correspond to the one or more condition quantities related to the response quantity under consideration, e.g. the temperature at the predetermined observation point is within a temperature range related to the response quantity.

[0097] A computer program according to an exemplifying and non-limiting embodiment comprises computer executable instructions for controlling programmable processing equipment to carry out actions related to a method according to any of the above-described exemplifying and non-limiting embodiments.

[0098] A computer program according to an exemplifying and non-limiting embodiment comprises software modules for determining an efficiency index of a process that involves a use of a mechanical system. The software modules comprise computer executable instructions for controlling programmable processing equipment to:

[0099] - receive first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service,

[0100] - maintain a database containing predetermined response quantities each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system,

[0101] - repeatedly update, for each of the response quantities, a stress history quantity expressing number of stress cycles occurred in a time-trend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration, - repeatedly update a fatigue damage sum based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and

[0102] - form the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum as an additional efficiency parameter.

[0103] The software modules can be for example subroutines or functions implemented with programming tools suitable for the programmable processing equipment.

[0104] A computer program product according to an exemplifying and non-limiting embodiment comprises a computer readable medium, e.g. a compact disc “CD”, encoded with a computer program according to an exemplifying and non-limiting embodiment.

[0105] A signal according to an exemplifying and non-limiting embodiment is encoded to carry information defining a computer program according to an exemplifying and non-limiting embodiment.

[0106] The specific examples provided in the description given above should not be construed as limiting the scope and / or the applicability of the accompanied claims. Lists and groups of examples provided in the description given above are not exhaustive unless otherwise explicitly stated.

Claims

What is claimed is:

1. An apparatus (100) for determining an efficiency index of a process involving a use of a mechanical system, the apparatus comprising processing equipment (103, 203) configured to receive first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service, characterized in that the apparatus comprises memory equipment (101 , 201 ) storing a database (102, 202) containing predetermined response quantities (Ri, ... , RQ) each being associated with one of predetermined stress ranges so that each of the response quantities expresses an upper limit for number of stress cycles at a predetermined observation point (111 ) of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system, wherein the processing equipment (103, 203) is configured to:- repeatedly update, for each of the response quantities, a corresponding stress history quantity (hi(t), ... , ho(t)) expressing number of stress cycles occurred in a time-trend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration,- repeatedly update a fatigue damage sum (D) based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and- form the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum.

2. An apparatus according to claim 1 , wherein the processing equipment is configured to form the efficiency index r| according to the formula:where Ci, C2, ... , and Cnare the efficiency parameters, S is the service, D is the fatigue damage sum, and a is a constant.

3. An apparatus according to claim 1 , wherein the processing equipment is configured to compute an estimate for a production rate (dS / dt) of the service, compute one or more estimates for one or more usage rates (dCi / dt, dC2 / dt, dCn / dt) of the one or more efficiency parameters, compute an estimate for a growth rate (dD / dt) of the fatigue damage sum, and form the efficiency index based on the estimates of the production rate of the service, the one or more usage rates of the efficiency parameters, and the growth rate of the fatigue damage sum.

4. An apparatus according to claim 3, wherein the processing equipment is configured to form the efficiency index r| according to the formula:where dCi / dt, dC2 / dt, ... and dCn / dt are the estimates of the usage rates of the efficiency parameters Ci , C2, ... and Cn, dS / dt is the estimate production rate of the service, dD / dt is the estimate of the growth rate of the fatigue damage sum, and 0 is a constant.

5. An apparatus according to any one of claims 1 -4, wherein each of the response quantities (R1 , ... , RQ) is a vector of response values so that each of the response values (Ni,i, ... , NP,Q) is associated with the predetermined stress range related to the corresponding response quantity and to one of predetermined mean stresses, and each of the response values expresses an upper limit for number of cycles of stress at the predetermined observation point of the mechanical system in a situation in which the cycles have the predetermined stress range related to the response quantity and the predetermined mean stress related to the response value under consideration, and each of the stress history quantities (hi(t), ... , ho(t)) is a vector of stress history values (ni,i(t), ... , np,o(t)) and the processing equipment (203) is configured to repeatedly update, for each of the response values, the corresponding stress history value expressing number of cycles occurred in thetime-trend of the stress and having the predetermined stress range and the predetermined mean stress related to the response value under consideration, and repeatedly update the fatigue damage sum (D) based on the response values and the stress history values related to the response values.

6. An apparatus according to claim 5, wherein the processing equipment is configured to compute the fatigue damage sum D according to the formula:D =y , N'Jwhere nij (t) is the stress history value expressing the number of the cycles occurred in the time-trend of the stress and having the ithpredetermined stress range and the jthpredetermined mean stress, and Ni is the response value relating to the ithpredetermined stress range and to the jthpredetermined mean stress.

7. An apparatus according to any one of claims 1 -6, wherein the processing equipment (103) is configured to repeatedly estimate the stress at the predetermined observation point (111 ) of the mechanical system based on data indicative of mechanical loading directed to the mechanical system.

8. An apparatus according to claim 7, wherein the processing equipment is configured to compute the stress as a weighted sum of i) membrane stress (om(t)) and ii) bending stress (ob(t)) acting on an area of the mechanical system a distance away from the predetermined observation point (111 ) of the mechanical system, weight factors of the weighted sum being predetermined local stress concentration factors (Kt,m, Kt,b) defined separately for the membrane and bending stresses.

9. An apparatus according to claim 8, wherein the processing equipment is configured to compute the membrane stress and the bending stress based on outputs (si(t), S2(t)) of strain gauges attached to the mechanical system, the membrane stress being proportional to an average of the outputs of the strain gauges and the bending stress being proportional to a difference of the outputs of the strain gauges.

10. An apparatus according to claim 9, wherein the apparatus comprises the strain gauges (104, 105).

11. An apparatus according to claim 7, wherein the processing equipment is configured to compute the stress based on forces directed to the mechanical system, an inverse of a stiffness matrix of a finite element model of at least a part of the mechanical system, and element equations of the finite element model expressing the stress as a function of nodal displacements of the finite element model.

12. An apparatus according to claim 11 , wherein the memory equipment is configured to store the inverse of the stiffness matrix of the finite element model and the processing equipment is configured to use the stored inverse of the stiffness matrix when repeatedly computing the stress.

13. An apparatus according to any one of claims 1 -12, wherein:- each of the response quantities is associated, in addition to the predetermined stress range, with one or more condition quantities descriptive of operating conditions of the mechanical system, and- the processing equipment is configured to update each stress history quantity to express number of cycles occurred in the time-trend of the stress so that the occurred cycles have the predetermined stress range related to the response quantity under consideration and the operating conditions of the mechanical system correspond to the one or more condition quantities related to the response quantity under consideration.

14. An apparatus according claim 13, wherein the one or more condition quantities descriptive of the operating conditions of the mechanical system comprise temperature at the predetermined observation point of the mechanical system.

15. An apparatus according to any one of claims 1 -14, wherein the second data is indicative of at least one of following efficiency parameters: energy consumed by the process, emissions produced by the process, amount of raw material consumed by the process, and waste produced by the process.

16. A method for determining an efficiency index of a process involving a use of a mechanical system, the method comprising:- receiving (301 ) first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service, characterized in that the method comprises:- maintaining (302) a database containing predetermined response quantities (Ri, ... , RQ) each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system,- repeatedly updating (303), for each of the response quantities, a corresponding stress history quantity (hi(t), ... , ho(t)) expressing number of stress cycles occurred in a time-trend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration,- repeatedly updating (304) a fatigue damage sum (D) based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and- forming (305) the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum.

17. A computer program for determining an efficiency index of a process involving a use of a mechanical system, the computer program comprising computer executable instructions for controlling programmable processing equipment to:- receive first data indicative of service produced by the process and second data indicative of one or more efficiency parameters needed for production of the service, characterized in that the computer program comprises computer executable instructions for controlling the programmable processing equipment to:- maintain a database containing predetermined response quantities (Ri, RQ) each being associated with one of predetermined stress ranges so that each of the response values expresses an upper limit for number of stress cycles at a predetermined observation point of the mechanical system in a situation in which the stress cycles have the predetermined stress range related to the response quantity under consideration, the upper limit corresponding to a predetermined survival probability of the mechanical system,- repeatedly update, for each of the response quantities, a corresponding stress history quantity (hi(t), ... , ho(t)) expressing number of stress cycles occurred in a time-trend of stress at the predetermined observation point and having the predetermined stress range related to the response quantity under consideration,- repeatedly update a fatigue damage sum (D) based on the response quantities and the stress history quantities related to the response quantities, the fatigue damage sum expressing cumulated fatigue damage of the mechanical system, and- form the efficiency index based on the service produced by the process, the one or more efficiency parameters, and the fatigue damage sum.

18. A non-volatile computer readable medium encoded with a computer program according to claim 17.

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