METHOD, CONTROLLER, AND COMPUTER PROGRAM PRODUCT FOR CONTROLLING A TARGET SYSTEM BY SEPARATELY TRAINING A FIRST AND A SECOND RECURRENT NEURAL NETWORK MODELS, WHICH ARE INITIALLY TRAINED USING OPARATIONAL DATA OF SOURCE SYSTEMS

BACKGROUND OF THE INVENTION

The control of complex dynamical technical systems, for in ^¬ stance gas turbines, wind turbines or other plants, can be optimized by means of so-called data driven approaches. With that, various aspects of such dynamical systems can be im ^¬ proved, e.g. for gas turbines their efficiency, combustion dynamics, or emissions, and e.g. for wind turbines their life-time consumption, efficiency, or yaw.

Modern data driven optimization utilizes machine learning methods for improving control strategies or policies of dy ^¬ namical systems with regard to general or specific optimiza ^¬ tion goals. Such machine learning methods often allow to out ^¬ perform conventional control strategies. In particular, if the controlled system is changing, an adaptive control ap ^¬ proach capable of learning and adjusting a control strategy according to the new situation and new properties of the dy ^¬ namical system is often advantageous over conventional non- learning control strategies.

However, in order to optimize complex dynamical systems, e.g. gas turbines or other plants, a sufficient amount of opera ^¬ tional data is to be collected in order to find or learn a good control strategy. Thus, in case of commissioning a new plant, upgrading or modifying it, it may take some time to collect sufficient operational data of the new or changed system before a good control strategy is available. Reasons for such changes might be wear, changed parts after a repair, or different environmental conditions.

Known methods for machine learning comprise reinforcement learning methods which focus on data efficient learning for a specified dynamical system. However, even when using these methods it may take some time until a good data driven con ^¬ trol strategy is available after a change of the dynamical system. Until then, the changed dynamical system operates outside a possibly optimized envelope. If the change rate of the dynamical system is very high, only sub-optimal results for a data driven optimization may be achieved since a suffi ^¬ cient amount of operational data may be never available. SUMMARY OF THE INVENTION

In view of the above, an object of the present invention is to create a method, a controller, and a computer program product for controlling a target system which allow a more rapid learning of control strategies in particular for a changing target system.

According to the present invention, a method, a controller, or a computer program product for controlling a target sys- tern, e.g. a gas or wind turbine or another technical system, is based on operational data of a plurality of source sys ^¬ tems. The method, controller, or computer program product is configured to receive the operational data of the source sys ^¬ tems, the operational data being distinguished by source sys- tern specific identifiers. By means of a neural network a neu ^¬ ral model is trained on the basis of the received operational data of the source systems taking into account the source system specific identifiers, where a first neural model com ^¬ ponent is trained on properties shared by the source systems and a second neural model component is trained on properties varying between the source systems. After receiving operational data of the target system, the trained neural model is further trained on the basis of the operational data of the target system, where a further training of the second neural model component is given preference over a further training of the first neural model component. The target system is controlled by means of the further trained neural network. Because the invention uses operational data of a plurality of source systems and uses neural models learned by means of these operational data one has a good starting point for a neural model of the target system. Actually, much less opera ^¬ tional data from the target system are needed in order to ob- tain an accurate neural model for the target system than in the case of learning a neural model for the target system from scratch. Hence, effective control strategies or policies can be learned in short time even for target systems with scarce data.

In a preferred embodiment of the invention the first neural model component may be represented by first adaptive weights, and the second neural model component may be represented by second adaptive weights. Such adaptive weights may also be denoted as parameters of the respective neural model compo ^¬ nent .

Preferably, the number of the second adaptive weights may be several times smaller than the number of the first adaptive weights. Because the training of the second neural model component represented by the second adaptive weights is given preference over the training of the first neural model compo ^¬ nent represented by the first adaptive weights, the number of weights to be adapted during the further training with the target system may be significantly reduced. This allows a more rapid learning for the target system.

Furthermore, the first adaptive weights may comprise a first weight matrix and the second adaptive weights may comprise a second weight matrix. The second weight matrix may be a diag ^¬ onal matrix. For determining adaptive weights of the neural model the first weight matrix may be multiplied by the second weight matrix.

According to a preferred embodiment, the first neural model component may be not further trained. This allows to focus on the training of the second neural model component reflecting the properties varying between the source systems.

Alternatively, when further training the trained neural mod ^¬ el, a first subset of the first adaptive weights may be sub ^¬ stantially kept constant while a second subset of the first adaptive weights may be further trained. This allows a fine tuning of the first neural network component reflecting the properties shared by the systems even during the further training phase.

According to a preferred embodiment of the invention the neu- ral model may be a reinforcement learning model, which allows an efficient learning of control strategies for dynamical systems .

Advantageously, the neural network may operate as a recurrent neural network. This allows for maintaining an internal state enabling an efficient detection of time dependent patterns when controlling a dynamical system. Moreover, many so-called Partially Observable Markov Decision Processes may be handled like so-called Markov Decision Processes by means of a recur- rent neural network.

According to a preferred embodiment of the invention it may be determined, during training of the neural model, whether the neural model reflects a distinction between the proper ^¬ ties shared by the source systems and the properties varying between the source systems. In dependence of that determina ^¬ tion the training of the neural model can be affected. In particular, the training of the neural model on the basis of the operational data of the source systems may be finished if such a distinction is detected with a predetermined reliabil ^¬ ity.

Moreover, policies or control strategies resulting from the trained neural model may be run in a closed learning loop with the technical target system.

Additional features and advantages of the present invention are described in, and will be apparent from the following De- tailed Description of the Invention and the Figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows a graphical illustration of an architecture of a recurrent neural network in accordance with an exemplary embodiment of the present invention.

Figure 2 shows a sketch of an exemplary embodiment of the in ^¬ vention comprising a target system, a plurality of source systems and a controller.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT According to the present invention a target system is controlled not only by means of operational data of that target system but also by means of operational data of a plurality of source systems. The target system and the source systems may be gas or wind turbines or other dynamical systems in ^¬ cluding simulation tools for simulating a dynamical system.

Preferably, the source systems are chosen to be similar to the target system. In that case the operational data of the source systems and a neural model trained by means of them are a good starting point for a neural model of the target system. With the usage of operational data or other infor ^¬ mation from other, similar technical systems the amount of operational data required for learning an efficient control strategy or policy for the target system can be reduced con ^¬ siderably. The inventive approach increases the overall data efficiency of the learning system and significantly reduces the amount of data required before a first data driven con ^¬ trol strategy can be derived for a newly commissioned target system.

According to a preferred embodiment of the invention a gas turbine should be controlled as a target system by means of a neural network pre-trained with operational data from a plu- rality of similar gas turbines as source systems. The source systems may comprise the target system at a different time, e.g. before maintenance of the target system or before ex ^¬ change of a system component etc.. Vice versa, the target system may be one of the source systems at a later time. The neural network is preferably implemented as a recurrent neu ^¬ ral network.

Instead of training a distinct neural model for each of the source systems separately, a joint neural model for the fami- ly of similar source systems is trained based on operational data of all systems. That neural model comprises as a first neural model component a global module which allows opera ^¬ tional knowledge to be shared across all source systems.

Moreover, the neural model comprises as a second neural model component source-system-specific modules which enable the neural model to fine-tune for each source system individual ^¬ ly. In this way, it is possible to learn better neural mod ^¬ els, and therefore, control strategies or policies even for systems with scarce data, in particular for a target system similar to the source systems.

Let source and ifarget denote two sets of s stern-speci fic identi ^¬ fiers of similar dynamical systems. The identifiers from the set jourc each identif one of the source systems while the identifiers from the set at _¾ r _t identify the target system. 11 is assumed that the source systems have been observed suffi ^¬ ciently long such that there is enough operational data available to learn an accurate neural model of the source systems while, in contrast, there is only a small amount of operational data of the target system available. Since the systems have similar dynamical properties, transferring knowledge from the well-observed source systems to the scarcely observed target system is an advantageous approach to improve the model quality of the latter.

Let ¾€ 5 denote an initial state of the dynamical systems considered where S denotes a state space of the dynamical systems , and let ¾»...»Sy denote a Γ-step sequence of actions with a _t € A being an action in an action space A of the dynamical systems at a time step t . Furthermore, let hi,...,h _T+ i denote a hidden state sequence of the recurrent neural net- work. Then a recurrent neural network model of a single dy ^¬ namical system, which yields a successor state sequence

S2,— ,8 j+i , may be defined by the following equations ¾ = + ¾)

where € i^ ¹¹ " is a weight matrix from layer u to layer v, the latter being layers of the recurrent neural network.

b _p € \SL ^V is a bias vector of layer v, n _v is the size of layer v and ( ·) is an elementwise nonlinear function, e.g. tanh(-) .

The W _uv and the b _v can be regarded as adaptive weights which are adapted during the learning process of the recurrent neu- ral network.

In order to enable knowledge transfer from the source systems to the target system, the state transition W _m h _t , which describes the temporal evolution of the states ignoring exter- nal forces , and the effect of an external force ¾ _a % may be modified in order to share knowledge common to all source systems while yet being able to distinguish between the pecu ^¬ liarities of each source system. Therefore, the weight matrix

¾ _¾ , is factored yielding

where z€ |% _» - _ι % _4Β „υ _{ί¾ £} ΐ1 is an Euclidean basis vector having a "1" at the position i i _5aatiX U /tngit ^an d " 0 "s elsewhere. I.e. the vector z carries the information by means of which the recurrent neural network can distinguish the specific source systems . In consequence, z acts as a column selector of W^ _z . such that there is a distinct set of parameters al located for each source system. The transformation is therefore a composition of the adaptive weights l<¾¾ and 1¾ _& , which are shared among all source systems, and the adaptive weights ΐ¾ζ speci fic to each source system.

The same factori zation technique is appl ied to ¾ _fl yielding

» W dmg{W _faS z)W _faM .

The resulting factored tensor recurrent neural network is then described by the following equations:

Thus, the adaptive weights W _hfn , l¾ _ft , W _hfar W _faa , b _hl W _sh/ and b _s refer to properties shared by all source systems and the adaptive weights of the diagonal matrices diag ( W _fhz z) and diag(I¥ _az z) refer to properties varying between the source systems . I.e. the adaptive weights ¾ _¾ , W _hfa , W _faa , b _h , W _S h, and b _s represent the first neural model component while the adaptive weights diag ( W _fhz z) and diag(I¥ _az z) represent the second neural model component. As the latter adaptive weights are diagonal matrices they comprise much less parameters than the first adaptive weights. I.e. the training of the second neural model component requires less time and/or less operational data than the training of the first neural model component.

Figure 1 illustrates a graphical representation of the fac- tored tensor recurrent neural network architecture described above. The dotted nodes in figure 1 indicate identical nodes which are replicated for convenience. The nodes having the 0-symbol in their centers are "multiplication nodes", i.e. the input vectors of the nodes are multiplied component-wise. The standard nodes, in contrast, imply the summation of all input vectors. Bold bordered nodes indicate the use of an ac ^¬ tivation function, e.g. "tanh" (·) ·

Apart from the above described factorizations of the weight matrices additional or alternative representations may be used . E.g.:

- The weight matrices i¾¾ , W _fkhr W _hfa , and/or W _faa may be re ^¬ stricted to symmetric form.

- A system specific matrix diag ( W _fhz z) may be added to the weight matrix W _hh shared by the source systems. The latter may be restricted to a low rank representation

W _hh W _hu W _uh . Moreover, the W _uh may be restricted to symmet- ric form.

- The bias vector i¾ may be made system specific, i.e. depend on z . - When merging information of multiple source or target sys ^¬ tems into a neural model, issues may occur due to

miscalibrated sensors from which the operational data are de ^¬ rived or by which the actions are controlled. In order to cope with artifacts resulting from miscalibrated sensors the weight matrix W _S h and/or the bias vector b _s may be made sys ^¬ tem specific, i.e. depend on the vector z. In particular, these weight matrices may comprise a z-dependent diagonal ma- trix.

Figure 2 shows a sketch of an exemplary embodiment of the in ^¬ vention comprising a target system TS, a plurality of source systems S1,...,SN, and a controller CTR. The target system TS may be e.g. a gas turbine and the source systems S1,...,SN may be e.g. gas turbines similar to the target system TS.

Each of the source systems S1,...,SN is controlled by a rein ^¬ forcement learning controller RLC1 , RLC2 , or RLCN, respec- tively, the latter being driven by a control strategy or pol ^¬ icy P1,P2,..., or PN, respectively. Source system specific op ^¬ erational data DATl,..., DATN of the source systems S1,...,SN are stored in data bases DB1,...,DBN. The operational data DATl,..., DATN are distinguished by source system specific identifiers ID1 , IDN from / _saurc „ . Moreover, the respective operational data DATl , DAT2 , or DATN, are processed according to the respective policy P1,P2,..., or PN in the respective reinforce ^¬ ment learning controller RLC1 , RLC2 , or RLCN. The control output of the respective policy P1,P2,..., or PN is fed back into the respective source system SI,..., or SN via a control loop CL, resulting in a closed learning loop for the respec ^¬ tive reinforcement learning controller RLC1 , RLC2 , or RLCN.

Accordingly, the target system TS is controlled by a rein- forcement learning controller RLC driven by a control strate ^¬ gy or policy P. Operational data DAT specific to the target system TS are stored in a data base DB . The operational data DAT are distinguished from the operational data DATl DATN of the source systems S1,...,SN by a target system specific identifier ID from ί¾ι¾Λ· Moreover, the operational data DAT are processed according to the policy P in the reinforcement learning controller RLC . The control output of the policy P is fed back into the target system TS via a control loop CL, resulting in a closed learning loop for the reinforcement learning controller RLC.

The controller CTR comprises a processor PROC, a recurrent neural network RNN, and a reinforcement learning policy gen ^¬ erator PGEN. The recurrent neural network RNN implements a neural model comprising a first neural model component NM1 to be trained on properties shared by all source systems S1,...,SN and a second neural model component NM2 to be trained on properties varying between the source systems S1,...,SN, i.e. on source system specific properties.

As already mentioned above, the first neural model component NM1 is represented by the adaptive weights W _hfar Wfaar &hr ^sh, and b _s while the second neural model component NM2 is represented by the adaptive weights diag ( Wf _hz z) and diag ( W _faz z) .

By means of the recurrent neural network RNN the reinforce ^¬ ment learning policy generator PGEN generates the policies or control strategies ΡΙ,.,.,ΡΝ, and P. A respective generated policy ΡΙ,.,.,ΡΝ, P is then fed back to a respective reinforce ^¬ ment learning controller RLC1 , RLCN, or RLC, as indicated by means of a bold arrow FB in figure 2. With that, a learning loop is closed and the generated policies ΡΙ,.,.,ΡΝ and/or P are running in closed loop with the dynamical systems S1,...,SN and/or TS. The training of the recurrent neural network RNN comprises two phases. In a first phase, a joint neural model is trained on the operational data DAT1 , DATN of the source systems S1,...,SN. For this purpose, the operational data DAT1 , DATN are transmitted together with the source system specific identifiers ID1,...,IDN from the databases DB1,...,DBN to the controller CTR. In this first training phase the first neural model component NM1 is trained on properties shared by all source systems S1,...,SN and the second neural model component NM2 is trained on properties varying between the source sys ^¬ tems S1,...,SN. Here, the source systems S1,...,SN and their op ^¬ erational data DAT1 , DATN are distinguished by means of the systern-speci fic identifiers ID1 , IDN from sour e represented by the vector z .

In a second phase the recurrent neural network RNN is further trained by means of the operational data DAT of the target system TS. Here, the shared parameters !*¾¾, W _hfa , W _faar bhr ^sh, Ά ά b _s representing the first neural model component NM1 and adapted in the first phase are reused and remain fixed while the system specific parameters diag ( W _fh∑ z) and diag(I¥ _az z) representing the second neural model component NM2 are further trained by means of the operational data DAT of the target system TS. The recurrent neural network RNN distinguishes the operational data DAT of the target system TS from the operational data DAT1 , DATN of the source sys ^¬ tems S1,...,SN by means of the target system specific identifi ^¬ er ID. Due to the fact that the general structure of the dynamics of the family of similar source systems S1,...,SN is learned in the first training phase, adapting the system specific parameters of a possibly unseen target system TS can be completed within seconds despite a high complexity of the overall mod ^¬ el. At the same time, only little operational data DAT are required to achieve a low model error on the target system TS . In addition, the neural model of the target system TS is more robust to overfitting, which appears as a common problem when only small amounts of operational data DAT are availa ^¬ ble, compared to a model that does not exploit prior

knowledge of the source systems S1,...,SN. With the present in ^¬ vention only the peculiarities in which the target system TS differs from the source systems S1,...,SN remain to be deter ^¬ mined .

There are a number of ways to design the training procedures in order to obtain knowledge transfer from source systems S1,...,SN to the target system TS including but not limited to the following variants:

Given a joint neural model which was trained on operational data DAT1 , DATN from a sufficient number of source systems S1,...,SN, and given a new target system TS which is similar to the source systems S1,...,SN on which the joint neural model was trained, it becomes very data-efficient to obtain an ac ^¬ curate neural model for the similar target system TS. In this case, the shared parameters W _hfh , W _fflh , W _hfar W _faar b _h , W _shr and b _s of the joint neural model can be frozen and only the systems specific parameters diag ( W _fhz z) and diag (W _faz z) are further trained on the operational data DAT of the new target system TS. Since the number of system specific parameters is typically very small, only very little operational data is required for the second training phase. The underlying idea is that the operational data DAT1 , DATN of a sufficient num ^¬ ber of source systems S1,...,SN used for training the joint neural model contain enough information for the joint neural model to distinguish between the general dynamics of the fam ^¬ ily of source systems S1,...,SN and the source system specific characteristics. The general dynamics are encoded into the shared parameters l% _fe , W _hfa , W _faar b _h , W _shr and b _s allow- ing efficient transfer of the knowledge to the new similar target system TS for which only the few characteristic as ^¬ pects need to be learned in the second training phase.

For a new target system TS which is not sufficiently similar to the source systems S1,...,SN on which the joint model was trained, the general dynamics learned by the joint neural model may differ too much from the dynamics of the new target system TS in order to transfer the knowledge to the new target system TS without further adaption of the shared parame- ters . This may also be the case if the number of source sys ^¬ tems S1,...,SN used to train the joint neural model is too small in order to extract sufficient knowledge of the general dynamics of the overall family of systems. In both cases, it may be advantageous to adapt the shared adaptive weights W _hfh , W _hfa , W _faar b _h , W _sh/ and b _s also during the second training phase. In this case the opera ^¬ tional data DAT1 , DATN used for training the joint neural model are extended by the operational data DAT from the new target system TS and all adaptive weights remain free for adaption also during the second training phase. The adaptive weights trained in the first training phase of the joint neu ^¬ ral model are used to initialize a neural model of the target system TS, that neural model being a simple extension of the joint neural model containing an additional set of adaptive weights specific to the new target system TS. Thus, the time required for the second training phase can be significantly reduced because most of the parameters are already initial- ized to good values in the parameter space and only little further training is necessary for the extended joint neural model to reach convergence. Variations of that approach include freezing a subset of the adaptive weights and using subsets of the operational data DAT1 , DATN, DAT for further training. Instead of initializing the extended joint neural model with the adaptive weights of the initial joint neural model, those adaptive weights may be initialized randomly, and the extended neural model may be further trained from scratch with data from all systems

SI, SN, and TS .

The invention allows to leverage information or knowledge from a family of source systems S1,...,SN with respect to sys ^¬ tem dynamics enabling data-efficient training of a recurrent neural network simulation for a whole set of systems of simi ^¬ lar or same type. This approach facilitates a jump-start when deploying a learning neural network to a specific new target system TS, i.e. it achieves a significantly better op ^¬ timization performance with little operational data DAT of the new target system TS compared to a learning model without such a knowledge transfer. Further advantages of such information sharing between learning models for similar systems comprise a better adjustabil ^¬ ity to environmental conditions, e.g. if the different sys ^¬ tems are located within different climes. The learning model could also generalize towards different kinds of degradation, providing improved optimization capabilities for rare or uncommon situations because the combined information, gathered from all systems can be utilized.