Nimat Ullah
email: nimatullah09@gmail.com

Jan Treur
email: j.treur@vu.nl

An Adaptive Causal Network Model for Therapeutic Intervention for Regaining Cognitive Control

Keywords: adaptive causal modeling, negative metaplasticity, positive metaplasticity, mindfulness, cognition, therapy, reappraisal

Long term stress often causes depression and neuronal atrophies that in turn can lead to a variety of health problems. As a result of these cellular changes, also molecular changes occur. These changes, that include increase of glucocorticoids and decrease of the brain-derived neurotrophic factor, have the unfortunate effect that they decrease the cognitive abilities needed for the individual to solve the stressful situation. Such cognitive abilities like reappraisal and their adaptation mechanisms turn out to be substantially impaired while they are needed for regulation of the negative emotions. However, antidepressant treatments and some other therapies have proved to be quite effective for the strengthening of such cognitive abilities. This study introduces an adaptive causal network model for this phenomenon where a subject loses his or her cognitive abilities (negative metaplasticity) due to long-term stress and re-improve these cognitive abilities (positive metaplasticity) through mindfulness-based cognitive therapy (MBCT). Simulation results have been reported for demonstration of the phenomenon.

Introduction

Potentially, there can be various reasons and forms of cognitive alteration such as decline in cognitive abilities with age where the rate of decline varies from person to person [START_REF] Verhaeghen | Cognitive processes and ageing[END_REF]. The decline can be due to long-term stress [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF] or due to reduction of flexibility as the person grows older [START_REF] Charles | Strength and vulnerability integration: A model of emotional well-being across adulthood[END_REF]). This paper, specifically focuses on the consequences caused by long-term stress. Stress has become one of the most common negative emotion these days. Various studies have found that long-term stress can have very severe consequences [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF]; [START_REF] Mazure | Stressful life events interacting with cognitive/personality styles to predict late-onset major depression[END_REF][START_REF] Tennant | Work-related stress and depressive disorders[END_REF]). These studies highlight the cognitive decline as one of the main consequences of long-term stressors. Decrease in the brain-derived neurotrophic factor (BDNF) as a result of increase in the glucocorticoids was found to be the main reason of cell loss and hence the alteration in synaptic plasticity at a cellular level [START_REF] Fuchs | In vivo neurogenesis in the adult brain: regulation and functional implications[END_REF][START_REF] Sapolsky | Glucocorticoids, stress, and their adverse neurological effects: relevance to aging[END_REF]). However, there are a number of studies like [START_REF] Garland | The role of mindfulness in positive reappraisal[END_REF][START_REF] Garland | Positive Reappraisal Mediates the Stress-Reductive Effects of Mindfulness: An Upward Spiral Process[END_REF]) who put forward that mindfulness-based cognitive therapy (MBCT) combining different techniques from therapies and training helps in strengthening cognitive abilities, specifically those impaired by long-term stress. It works by focusing on present moment, gaining awareness of one's self and accepting the reality. This study considers MBCT instead of standard CBT, being one of the most studied therapies, due to the fact that some studies like [START_REF] Troy | History of Mindfulness-Based Cognitive Therapy Is Associated with Increased Cognitive Reappraisal Ability[END_REF]) have compared MBCT and CBT in terms of their performance and found that MBCT is more effective.

Moreover, this study considers an adaptive causal network modeling approach [START_REF] Treur | Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models[END_REF]) to model the above mentioned phenomena because stressful emotions and their effects form an adaptive and cyclic process which this approach particularly handles quite effectively as demonstrated, for example, in [START_REF] Ullah | Better Late than Never: A Multilayer Network Model Using Metaplasticity for Emotion Regulation Strategies[END_REF]; Ullah and Treur 2019). This modeling approach can be considered as a branch in the causal modeling area which has a long tradition in AI; e.g., see [START_REF] Kuipers | Commonsense reasoning about causality: Deriving behavior from structure[END_REF]; [START_REF] Kuipers | How To Discover a Knowledge Representation for Casual REasoning by Studying an Expert Pysician[END_REF][START_REF] Pearl | Causality[END_REF]). It distinguishes itself by a dynamic perspective on causal relations, according to which causal relations exert causal effects over time, and in addition these causal relations themselves can change over time as well. The basic type of network model used is called a multilevel adaptive temporal-causal network model. By adding dynamics an adaptation to causal modeling, applications become possible that otherwise would be out of reach of causal modeling. This provides a useful approach to translate (supported by a dedicated modeling environment) qualitative processes as known from empirical literature into adaptive causal network models that can be used for simulation.

In the rest of the paper, Sect. 2 gives brief account of the literature on the subject, Sect. 3 presents the adaptive cognitive network model which is explained by simulation results in detail in Sect. 4. Finally, the paper is concluded in Sect. 5.

Background Literature

Research on stress, being one of the common negative emotions, has come up with vital long lasting negative consequences of it [START_REF] Mazure | Stressful life events interacting with cognitive/personality styles to predict late-onset major depression[END_REF][START_REF] Tennant | Work-related stress and depressive disorders[END_REF]). Studies like [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF]) have shown its contribution to depression and the adaptive casual way it affects one's cognitive abilities. It's worth noting here that the structural and functional changes brought about by stress are similar to those of depression. At a cellular level, stress and depression cause cell and neuronal losses. By [START_REF] Sapolsky | Glucocorticoids, stress, and their adverse neurological effects: relevance to aging[END_REF]) such cellular changes in the hippocampus are linked to the increase in plasma levels of glucocorticoid hormones like cortisol. At a molecular level, the cellular deficiencies were found to take place at the hippocampus. This happens most of the time due to the decrease in the expression of the brainderived neurotrophic factor (BDNF) associated with elevation of glucocorticoids [START_REF] Fuchs | In vivo neurogenesis in the adult brain: regulation and functional implications[END_REF][START_REF] Sapolsky | Glucocorticoids, stress, and their adverse neurological effects: relevance to aging[END_REF]). Similarly, [START_REF] Smith | Stress and glucocorticoids affect the expression of brain-derived neurotrophic factor and neurotrophin-3 mRNAs in the hippocampus[END_REF]) also support the notion that high levels of glucocorticoids induced by stress and its administration are considered to be down-regulating the hippocampal expression. [START_REF] Mocchetti | Glucocorticoids differentially increase nerve growth factor and basic fibroblast growth factor expression in the rat brain[END_REF]) considers the reduction of BDNF, which supports neuronal survival and function in the hippocampus, as the potential mediating action of glucocorticoid on hippocampus. The effect of the boost of glucocorticoids is referred to as negative metaplasticity as it downregulates adaptivity of the hippocampal synaptic connectivity. In contrast, the boost in the expression of BDNF is referred to as positive metaplasticity as it strengthens adaptivity of the connectivity in the hippocampus. As a result of these changes, the subject loses his control of cognitive abilities and is unable to efficiently regulate his emotions in an adaptive manner. On the other hand, the same mechanisms can reversibly be used via treatment as well [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF], i.e., through the increase in the expression of BDNF. Synapses are responsible for the processing and transmission of neural information with some efficacy and their alteration is referred to as 'synaptic plasticity', which is a form of (firstorder) adaptation. The mechanisms described above indicate how synaptic plasticity itself also can change, which is a form of second-order adaptation usually called metaplasticity. When metaplasticity enhances the adaptive cognitive function, by [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF] it is called positive metaplasticity and if this change brings some impairment to the adaptive cognitive function, then it's referred to as negative metaplasticity this indeed has been observed in case of long-term stress [START_REF] Foster | Involvement of hippocampal synaptic plasticity in age-related memory decline[END_REF]; Kim and Yoon 1998); similar cognitive impairment has been observed in various other studies in both humans [START_REF] Lupien | Stress-induced declarative memory impairment in healthy elderly subjects: relationship to cortisol reactivity[END_REF]) and animals [START_REF] Mizoguchi | Chronic stress induces impairment of spatial working memory because of prefrontal dopaminergic dysfunction[END_REF].

Cognitive reappraisal, as a strategy, is considered to be a very adaptive strategy which contributes to positive psychological health by reducing negative effects and it is associated to improved memory and interpersonal functioning in contrast to, for example, suppression [START_REF] Butler | The social consequences of expressive suppression[END_REF][START_REF] Gross | Individual differences in two emotion regulation processes: Implications for affect, relationships, and well-being[END_REF][START_REF] John | Healthy and Unhealthy Emotion Regulation: Personality Processes, Individual Differences, and Life Span Development[END_REF]).

To deal with the cognitive decline caused by long-term stressors, we consider Mindfulness-based cognitive therapy (MBCT) as found quite effective by various researchers in this domain [START_REF] Garland | The role of mindfulness in positive reappraisal[END_REF][START_REF] Garland | Positive Reappraisal Mediates the Stress-Reductive Effects of Mindfulness: An Upward Spiral Process[END_REF]). The purpose of MBCT is to improve psychological health by increasing mindfulness. This therapy combines Kabat-Zinn's (kabat-Zinn 1990) mindfulness-based stress reduction program with the techniques used in Cognitive Behavior Therapy (CBT). Kabat-Zinn's Mindfulness-Based stress reduction program involves daily meditation and self-awareness exercises. The MBCT training program aims at promoting acceptance of thoughts/feelings without being judgmental, focusing on the present moment and awareness of one's self [START_REF] Coffey | Deconstructing Mindfulness and Constructing Mental Health: Understanding Mindfulness and its Mechanisms of Action[END_REF]). According to [START_REF] Allen | Mindfulness-based psychotherapies: a review of conceptual foundations, empirical evidence and practical considerations[END_REF]) practicing of acceptance is meant to develop the ability to distinguish oneself from the contents of negative thoughts and recognize that emotions are non-permanent events. This is achieved by bringing a person in a decentered metacognitive state which may help in increasing cognitive flexibility through disengagement from the initial negative thoughts/appraisal, as has been considered essential by [START_REF] Garland | The role of mindfulness in positive reappraisal[END_REF]). After disengagement comes the ability to successfully switch from negative appraisal to positive appraisal and previous research credits this ability to mindfulness training [START_REF] Jha | Mindfulness training modifies subsystems of attention[END_REF]). Similarly, MBCT encourages individuals to focus on the present moment as it is expected to give insight into one's own (wide range of) stimuli related physical sensations, feelings and thoughts. Otherwise, chances of failure increase in the reappraisal/re-interpretation of the thoughts without knowing about it.

Multilevel Adaptive Cognitive Modeling

This section of the paper gives overview of the multilevel adaptive causal network modeling approach [START_REF] Treur | Network-Oriented Modeling: Addressing Complexity of Cognitive, Affective and Social Interactions[END_REF][START_REF] Treur | Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models[END_REF]) that has been used for development and simulation of the adaptive causal network model. Table 1 summarizes the main conceptual and numerical representations for this adaptive causal modeling approach. The Network-oriented modeling approach provides a library of over 36 combination functions. Apart from the available combination functions, self-defined combination functions can also be added to the library which makes the approach quite flexible and supports a wide application range. The aggregated causal impact of multiple states Xi on Y at t, is determind using combination function cY(..)

Timing of the causal effect

Y(t+Dt) = Y(t) + hY [aggimpactY(t) -Y(t)] Dt = Y(t) + hY [cY(wX 1,Y X1(t), …, wX k,Y Xk(t)) -Y(t)] Dt
The causal impact on Y is exerted over time gradually, using speed factor hY; here the Xi are all states with outgoing connections to state Y Table 2 provides explanation of the various states of the adaptive causal network model proposed in this paper. In the table and the figure, the background colors differentiate between the (adaptation) levels of the model and are part of the meaning; they are called reification levels as they explicitly represent by their states some of the network characteristics of the level below. For instance, the base model has 17 states, the first reification level modeling synaptic plasticity (first-order adaptation) has 1 state and the second reification level modeling metaplasticity (second-order adaptation) has 2 states. The modeled synaptic plasticity at the first reification level is addressed by the (adaptive) connection weight wfs b ,cs reapp by representing it by reification state Wfs b ,cs reapp . The metaplasticity concerning adaptation of the dynamics of the adaptation of this connection weight is addressed by the second-level reification states 𝐌 𝐖 #$ % , '$()*++ for the persistence of the learnt effects and 𝐇 𝐖 #$ % , '$()*++ for the speed of the adaptation process. The connectivity picture of the model shown in Fig. 1 demonstrates the phenomenon where long-term stress causes negative metaplasticity of cognitive abilities, i.e. loss in the ability to use and adapt cognitive reappraisal for regulation of negative emotions. In contrast, mindfulness-based cognitive therapy has been used as an intervention to obtain positive metaplasticity through which upregulation of the cognitive reappraisal ability can take place. In Fig. 1, the bottom level represents the base model which performs the basic function of regulation of emotions through reappraisal. Cognitive reappraisal changes one's perception/belief about the stimulus: from a negative to a positive interpretation in this model. Generally, reappraisal can also be from positive believe to negative belief depending upon the demand of the situation, but in this model, reappraisal refers to the reinterpretation to positive belief from negative. The first reification level modeling first-order adaptation, represents Hebbian learning for the connection from base state fs 2 to base state cs =>?@@ . The dynamics of this state 𝐖 AB 2 , CB ()*++ represents the learning taking place for this connection at the base level. Learning doesn't only refer to increase in the strength of the connection, it can also involve decrease in the strength of the connection over time. In this model, as demonstrated in Figs. 2 and3, initially, this connection from fs 2 , to cs =>?@@ gets weaker due to long-term stress. When this connection gets weaker, the negative (body) feeling state fs 2 gets higher which activates the goal state gs 2 to address the problem, as also demonstrated in (Mohammadi Ziabari and Treur 2019) for such kind of interventions. This goal state represents the intention of the person to undergo some kind of therapy for getting back on track. In the scenario used for this model, goal activation refers to the intention to undergo MBCT (therapy) but in general it can be any kind of intervention, for example, antidepressant treatment as suggested in [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF]) etc.

The second-order reification states 𝐌 𝐖 #$ % , '$()*++ and 𝐇 𝐖 #$ % , '$()*++ represent the persistence factor µ and the speed factor h for 𝐖 AB 2 , CB ()*++ respectively. The 𝐌-state refers to how long or short the 𝐖-state retains its learned value. Similarly, the 𝐇-state controls the speed factor of the 𝐖-state managing how fast or slow the 𝐖-state learns of forgets the value. Change in the speed and persistence factor is referred to as metaplasticity. The upregulation is called positive while the downregulation is called negative metaplasticity.

The two boxes below give insight into the different dynamics of the network. The colors and the boxes itself are part of the meaning and standard defined by network oriented modeling approach in [START_REF] Treur | Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models[END_REF]). In the boxes below, Box 1 represent the role matrices mb and mcw. In role matrix mb, each state has a row which shows all the incoming connections to that state. It's worth mentioning here that in matrix mb each state has only the incoming connections which are either at the same level or come from a lower level. The downward connections are indicated in the other role matrices instead. For instance, in matrix mcw the state number X18 (i.e., the 𝐖-state) represents the adaptive connection from X9 to X 17 at the base level, the causal effect of which is modeled by the downward connection from X18. Moreover, the values between -1 and 1 in role matrix mcw represent the connection weights of the incoming connections to that specific state. The specific values in the role matrices allow to get the simulation pattern shown in Fig. 2 and Fig. 3. The values were chosen such that the simulation results exhibit a pattern similar to the ones found in the literature.

In Box 2, role matrices mcfw, mcfp and ms are given. Matrix mcfw indicates the combination function used at a state Xi for the aggregation of incoming causal impact from other states to state Xi. For instance, state X1 uses the identify function, state X18 uses the Hebbian combination function and state X19 uses alogistic(..) as combination function, defined by

𝐚𝐥𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝛔,𝛕 (𝑉 Q , … , 𝑉 S ) = [ Q Q:> W𝛔XY Z [⋯Y ] W^_ + Q Q:> 𝛔𝛕 ](1 + 𝑒 9𝛔𝛕 ) (1)
Moreover, the first-order adaptation state X18 uses the Hebbian learning combination function hebb(..) defined by

𝐡𝐞𝐛𝐛 𝛍 (𝑉 Q , 𝑉 h , 𝑊) = 𝑉 Q 𝑉 h (1 -𝑊) + 𝛍𝑊 (2)
Box 1 Role matrices for connectivity

Role matrix mcfp provides the parameter values for each of the combination function used as indicated in mcfw. In the row for X18, in column 2 (for Hebb) of mcfp, X19 in the red cell indicates the downward causal connection from the second-order reification state to X18. In other words, X19 is responsible for the persistence factor of X18. Similarly, the X20 in the red cell at the row for X18 in role matrix ms indicates the downward causal connection from the second-order reification level to the first-order reification level. In other words, X20 is responsible for the speed factor of X18. These downward causal connections are essential to causally effectuate the adaptation processes modeled as dynamics at the higher levels.

Simulation Results

This section of the paper explains the simulation results given in Fig. 2 and Fig. 3 obtained from the adaptive causal network model with connectivity depicted in Fig. 1

X19 𝐌 𝐖#$ % ,'$ ()*++ X9 X17 X18 X19 X19 𝐌 𝐖#$ % ,'$ ()*++ -1 1 1 1 X20 𝐇 𝐖#$ % ,'$ ()*++ X9 X17 X18 X20 X20 𝐇 𝐖#$ % ,'$ ()*++ -1 1 1 1
of the states are given below in Table 2. Fig. 2 demonstrates the basic phenomenon as discussed in the literature section, where long-term stressors decrease the adaptive cognitive abilities of the subject. The subject decides to undergo MBCT and regains his cognitive abilities. Fig. 2 shows the patterns for all the states at the base level. In the figure, it can be seen that initially the control state cs =>?@@ for reappraisal gets activated as soon as negative belief bs 9 gets higher. The control state cs =>?@@ changes the beliefs representing the interpretation of the person and, therefore, bs 9 decreases while bs : increases. But during this time, gradual decrease in the activation level of cs =>?@@ can be observed and that's the time when bs 9 also stays higher and bs : stays lower. In the meanwhile, gradual increase in the goal state gs 2 takes place, since as a result of decrease in the activation level of cs =>?@@ the intensity of negative feelings fs 2 increases which in turn activates the goal gs 2 to undergo some therapy to regain cognitive control. Goal state gs 2 activates the states that lay on the casual pathway describing undergoing MBCT therapy. Finally, when the execution state for goal (therapy) es 4 gets enough momentum, as a result cs =>?@@ again gets activated. This means that the person has regained his cognitive reappraisal ability during execution of the therapy; however, at this stage the person still depends on the therapy for this. While the person is again becoming able to reappraise his or her emotions with a little help from the therapy, due to the achieved lower levels of fs 2 , the negative metaplasticity at the second reification level turns into positive metaplasticity by increasing the too low values of the two secondorder states 𝐌 𝐖 #$ % , '$()*++ and 𝐇 𝐖 #$ % , '$()*++ to higher values. Therefore, now a learning process takes place (that was blocked before by the negative metaplasticity due to low values of 𝐌 𝐖 #$ % , '$()*++ and 𝐇 𝐖 #$ % , '$()*++ ), strengthening the connection from fs 2 to cs =>?@@ . Due to the successful reappraisal, fs 2 goes down, so it deactivates the goal gs 2 to undergo therapy. This deactivates the therapy but the person is still able to reappraise his emotions effectively as before. It means that overall the connection has re-strengthened as a result of MBCT. This figure represents two phases of the subject's life. First phase is before his cognitive abilities are impaired by long-term stress where he regulates his emotions multiple times during that phase. The second phase is after the therapy when he's again able to use his cognitive abilities. The fluctuation in the graphs represent the cyclic nature of the stressful emotions that takes place repeatedly in cycles and are regulated accordingly. This pattern is exactly as various researchers from cognitive and neuro-sciences have described in their articles as summarized in the background study in Sect. 2, for instance [START_REF] Garcia | Stress, Metaplasticity, and Antidepressants[END_REF]. Fig. 3 gives insight into the first and second-level reification states. The states represented in the figure are 𝐖 AB 2 , CB ()*++ , 𝐌 𝐖 #$ % , '$ ()*++ , 𝐇 𝐖 #$ % , '$ ()*++ which represent the adaptation of the indicated connection weight based on Hebbian learning, and the persistence factor and the speed factor for this adaptation, respectively. First it is shown that all these three states decrease because of the long-term stressors, but after activation of the therapy in the base model all three states again get higher values. It's worth noting here that all the states stay high even after the therapy gets deactivated in the base model. This shows that the person's wellbeing does not depend on the therapy anymore.

As already mentioned, W represent the Hebbian learning taking place at the connection indicated by fs 2 , cs =>?@@ in the base model. The speed factor and persistence of the W is handled by the H and M-states respectively. In the Fig. 3 initially negative metaplasticity occurs (lower values of the second-order states) because of long-term stressors, so the learning gets blocked in a sense. Due to this, the connection fs 2 , cs =>?@@ gets weaker. But as the person undergoes MBCT, due to the positive effects that has on the second-order states 𝐌 𝐖 #$ % , '$()*++ and 𝐇 𝐖 #$ % , '$()*++ , the connection fs 2 , cs =>?@@ again gets stronger and the person is again able to reappraise his emotions even after there is no more therapy. These results in Fig. 2 and Fig. 3 are completely in line with the findings from cognitive and neurosciences.

Conclusion

In this paper, the ideas on negative and positive metaplasticity from the (empirical) literature have been modeled and given a concrete shape in the form of simulations. On one hand, the multi-order adaptive causal network model presented in this paper gives a concrete shape to the abstract ideas, on the other hand it also highlights the consequences of long-term stressors along with the possible treatment for the psychological problems they cause. Findings from various neurological and psychological studies were brought together and presented in the form of a concrete computational model. Various therapies have already been modeled in work like (Mohammadi Ziabari and Treur 2019), but this paper considers therapy as a permanent treatment to cope with negative metaplasticity for the first time.

The paper also shows how the applicability scope of causal modeling, which has a long tradition in AI (e.g., see [START_REF] Kuipers | Commonsense reasoning about causality: Deriving behavior from structure[END_REF][START_REF] Kuipers | How To Discover a Knowledge Representation for Casual REasoning by Studying an Expert Pysician[END_REF][START_REF] Pearl | Causality[END_REF])), can substantially be widened by adding dynamics and (multi-order) adaptation to causal modeling. Doing this, causal modeling becomes applicable to modeling of dynamic and adaptive processes that otherwise would be out of reach for causal modeling. The introduced second-order adaptive network model provides a good basis to develop a patient model (based on a virtual agent) for virtual training of therapists. In future, the author aims at extending the model by incorporating more neurological states for both the negative and positive metaplasticity and the neurological states involved in MBCT.

Fig. 1 .

 1 Fig. 1. Adaptive causal network model for therapeutic intervention for long-term stress

Fig. 2 .

 2 Fig. 2. Loss and gain of adaptive cognitive abilities as a result of long-term stressor (base level)

Fig. 3 .

 3 Fig. 3. First and second-order reification states for plasticity and metaplasticity over time

Table 1 .

 1 Conceptual and numerical representations for the adaptive causal modeling approach

	Concept	Conceptual Representation	Explanation
	States and connections	X, Y, X®Y	Describes the nodes (representing states) and links
			(representing causal connections between states)
			of the network structure
	Connection weight	wX,Y	The connection weight wX,Y Î [-1, 1] represents the
			strength of the causal impact of state X on state Y
			through connection X®Y
	Aggregating multiple
	impacts on a state
	Aggregating multiple	aggimpactY(t)
	causal impacts

cY(..)

For each state Y (a reference to) a combination function cY(..) is chosen to combine the causal impacts of other states on state Y Timing of the effect of causal impact hY For each state Y a speed factor hY ³ 0 is used to represent how fast a state is changing upon causal impact concept numerical representation explanation State values over time t Y(t) At each time point t each state Y in the model has a real number value in [0, 1] Single causal impact impactX,Y(t) = wX,Y X(t) At t state X with a connection to state Y has an impact on Y, using connection weight wX,Y = cY(impactX 1,Y (t),…, im-pactX k,Y (t)) = cY(wX 1,Y X1(t), …, wX k,Y Xk(t))

Table 2 .

 2 Overview of the states of the multi-level network model in Fig.1

		State	Explanation	Level
	X1	ws /	World state for stimulus 's'
	X2	ss /	Sensor state for stimulus 's'
	X3	srs /	Sensory representation state for stimulus 's'
	X4	gs 2	Goal state for body 'b'
	X5	ps 4	Preparation state for goal 'g'
	X6	es 4	Execution state for goal 'g'
	X7	ss 6	Sensor state for body state b
	X8	srs 2	Sensory representation state for body sate b	Base level
	X9	fs 2	Feeling state for body state b
	X10	ps 2	Preparation state for body state b
	X11	es 2	Expression execution state for body state b
	X12	bs 9	Belief state for negative belief -
	X13	bs :	Belief state for positive belief +
	X14	accp 2	Acceptance state for body
	X15	aw 2	Awareness state for body
	X16	pr

2 Present moment state of body X17 cs =>?@@ Control state for cognitive reappraisal X18 𝐖 AB 2 , CB ()*++ Reified representation state for connection weight wfs b ,cs reapp First Reification Level X19 𝐌 𝐖 #$ % , '$()*++ Reified representation state for persistence factor µ for Wfs b ,cs reapp Second Reification Level X20 𝐇 𝐖 #$ % , '$()*++ Reified representation state for speed factor h for Wfs b ,cs reapp

  . These results were obtained using the values in Box 1 and Box 2. Moreover, initial values

	mb connectivity:				mcw connectivity:
			1	2	3	4		1	2	3	4
	base connectivity				connection weights
	X1	ws /	X1			X1	ws /	1
	X2	ss /	X1			X2	ss /	1
	X3	srs /	X2			X3	srs /	1
	X4	gs 2	X9			X4	gs 2	0.8
	X5	ps 4	X4			X5	ps 4	1
	X6	es 4	X14	X15	X16	X6	es 4	0.5	0.5	0.58
	X7	ss 6	X11			X7	ss 6	1
	X8	srs 2	X7	X10		X8	srs 2	0.27	0.3
	X9	fs 2	X8			X9	fs 2	1
	X10	ps 2	X9	X12		X10	ps 2	0.1	0.45
	X11	es 2	X10			X11	es 2	1
	X12	bs 9	X3	X13	X17	X12	bs 9	0.6	-0.4	-0.21
	X13	bs :	X3	X12		X13	bs :	0.4	-0.35
	X14	accp 2	X5	X9		X14	accp 2	0.9	0.2
	X15	aw 2	X5	X9		X15	aw 2	0.9	0.2
	X16	pr 2	X5	X9		X16	pr 2	0.9	0.2
	X17	cs =>?@@	X6	X9	X12	X17	cs =>?@@	1	X18	0.2
	X18	𝐖 AB 2 , CB()*++	X9	X17	X18	X18	𝐖 AB 2 , CB()*++	1	1	1

Table 3 .

 3 Initial values serving as inputs to the states Wfs b ,cs reapp HW fsb,csreapp MW fsb,csreapp

	State	wss	All other base states
	Initial value	1	0	0.3	0.5	0.9


Saba Gul
email: sabagul@uetpeshawar.edu.pk

Gul Muhammad Khan

Forecasting Hazard Level of Air Pollutants Using LSTM's

Keywords: Air pollution, AQI, Forecasting, LSTM's

The South Asian countries have the most polluted cities in the world which has caused quite a concern in the recent years due to the detrimental effect it had on economy and on health of humans and crops. PM 2.5 in particular has been linked to cardiovascular diseases, pulmonary diseases, increased risk of lung cancer and acute respiratory infections. Higher concentration of surface ozone has been observed to have negatively impacted agricultural yield of crops. Due to its deleterious impact on human health and agriculture, air pollution cannot be brushed off as a trivial matter and measures must be taken to address the problem. Deterministic models have been actively used; but they fall short due to their complexity and inability to accurately model the problem. Deep learning models have however shown potential when it comes to modeling time series data. This article explores the use of recurrent neural networks as a framework for predicting the hazard levels in Lahore, Pakistan with 95.0% accuracy and Beijing, China with 98.95% using the time series data of air pollutants and meteorological parameters. Forecasting air quality index (AQI) and Hazard levels would help the government take appropriate steps to enact policies to reduce the pollutants and keep the citizens informed about the statistics.

Introduction

Air pollution has been brushed off for quite some time as a trivial subject but the current research suggest the relentless damage it can cause humans and crop yield. In particular the cities of South Asian countries such as China and India have made to the list of most polluted cities and the cities of Pakistan are joining the list due to increase in levels of particulate matter and toxic fumes from the industries [17].

Exposure to higher concentration of surface ozone can trigger allergic reactions such as asthma and cause inflammation of air ways due to oxidative stress Supported by NCAI, UET-P [START_REF] Kim | A review on human health perspective of air pollution with respect to allergies and asthma[END_REF], [START_REF] Kelly | Oxidative stress: its role in air pollution and adverse health effects[END_REF]. PM2.5 has been associated with 4 to 8% increase in cardiopulmonary diseases and lung cancer [START_REF] Pope | Lung cancer, cardiopulmonary mortality, and long-term exposure to fine particulate air pollution[END_REF]. Air pollution has been linked to cardiovascular diseases in urban communities. Most of the hospitalized patients suffering from diseases like angina, myocardial infarction and heart failure have been put in such a situation, due to the long-term exposure to combustion-derived nano-particles that incorporate reactive organic and transition metal components [START_REF] Mills | Adverse cardiovascular effects of air pollution[END_REF]. Moreover, studies suggest that high concentration of surface ozone has a detrimental effect on crop yield [START_REF] Chuwah | Global impacts of surface ozone changes on crop yields and land use[END_REF], [START_REF] Lin | Impacts of O3 on premature mortality and crop yield loss across China[END_REF]. In recent years, due to increase in awareness of the bleak consequences of air pollutants, forecasting of air pollutants and their impact on human and crops has become an active area of research. Several deterministic and non-deterministic models were explored to model the behavior of pollutants [START_REF] Reddy | Deep Air: Forecasting Air Pollution in Beijing, China[END_REF], [START_REF] Bai | Air pollution forecasts: An overview[END_REF]. Deep leaning models have had quite some success when it comes to modeling the problem and forecasting air pollutants. The meteorological parameters due to their conducive behaviour in pollutant dissemination and pollutant concentrations were used to forecast Hazard levels. Since the parameters used for modeling are time series, so the recurrent neural networks, Long Short Term Memory (LSTM) networks are employed due to their ability to accurately capture temporal trends [START_REF] Le | Real-time Air Pollution prediction model based on Spatiotemporal Big data[END_REF], [START_REF] Soh | Adaptive Deep Learning-Based Air Quality Prediction Model Using the Most Relevant Spatial-Temporal Relations[END_REF], [START_REF] Reddy | Deep Air: Forecasting Air Pollution in Beijing, China[END_REF]. The two major contributions of this article are the following:

1. Provide a dataset comprising of Lahore, Pakistan meteorological and pollutants statistics. 2. Employ deep learning model to develop a forecasting and classification system for assessing air quality.

Literature Survey

An LSTM model is trained in [START_REF] Han | A Bayesian LSTM Model to Evaluate the Effects of Air Pollution Control Regulations in China[END_REF] on sensor data of Aerosol Optical Depth (AOD), meteorology and particulate matter which can provide quite accurate prediction of the concentrations of harmful gases (80% PM 2.5 variability). The system has been successfully deployed in Beijing, China and has helped in bringing down the pollution in Beijing by 23%.

A supervised regression model is developed based on historical data of air pollution in Sydney [START_REF] Hu | SVR based dense air pollution estimation model using static and wireless sensor network[END_REF] which surpassed its contemporary ANN's in terms of accuracy in prediction and has high spatial resolution.

Forecasting air pollution is done through Multi-channel Ensemble framework through supervised extraction and learning which out performs its contemporary state of the art systems [START_REF] Zhang | Early Air Pollution Forecasting as a Service: An Ensemble Learning Approach[END_REF]. PM 2.5 , PM 10 , SO 2 , CO, NO x and ozone levels are predicted quite accurately.

In [START_REF] Yi | Deep distributed fusion network for air quality prediction[END_REF] attempts are made to model the complex relation between different parameters and its individual impact on pollutant levels using deep distribution fusion network while the spatial correlation is modelled using deep neural network. The system, deep air out performs ten state of the art baseline models and achieves an average accuracy of 81.1%, 63%, 46% in 1-6h, 7-48h, sudden changes when deployed in 300+ cities of China.

Real time air-pollution predication is carried out in Daegu city, Korea [START_REF] Le | Real-time Air Pollution prediction model based on Spatiotemporal Big data[END_REF] by processing the big data received from the air quality sensing modules installed on taxis. The spatial distribution of the pollutant levels is fed to a CNN model. For accurate processing of the temporal data; LSTM is used with a NN in parallel to cater for the meteorological factors effecting pollutant concentration. The testing results in an accuracy of 74% in real time over the data collected over a span of four months.

Spatial-temporal information is used in [START_REF] Soh | Adaptive Deep Learning-Based Air Quality Prediction Model Using the Most Relevant Spatial-Temporal Relations[END_REF] to predict air quality using a combination of neural networks called ST-DNN which attempts to model the correlations between several meteorological conditions, elevation space and PM levels. LSTM is used to model long term temporal relations i-e historical time series relation; CNN extracts the relationship between terrain information and pollutant levels while ANN is used with the current data and thereby models high frequency information. When evaluated on Taiwan and Beijing dataset, the network outperformed the baseline and comparative networks under consideration.

In order to enact policies to alleviate the pollution levels, accurate prediction is needed to carry out informed decisions. The temporal data of pollutants along with meteorological data is processed by a recurrent model [START_REF] Reddy | Deep Air: Forecasting Air Pollution in Beijing, China[END_REF], LSTM to forecast air pollutants since LSTMs have the ability to capture sequential relations. The frame work can predict air pollution 5-10 hours in the future quite well but as the future time steps are increased beyond 10 hours, we see degradation in performance. Since short term data of 6-10 hours is needed to predict future time steps, power consumption can be reduced by turning the sensors on at specific intervals to collect data.

Artificial neural network (ANN) is used to predict PM 10 concentration at 6 subways in Seoul, Korea [START_REF] Park | Predicting PM10 concentration in Seoul metropolitan subway stations using artificial neural network (ANN)[END_REF]. Due to impracticality of monitoring PM 10 directly at the crowded stations, PM 10 concentrations are obtained from public data service near subway stations (PM 10 out). In addition, it is observed that the shape and depth of the platform at the subway stations play an important role in influencing the model performance. The framework was able to predict PM 10 concentrations at the platforms with an accuracy 67-80% depending upon parameters; inflow of PM 10 (PM 10 in), outflow of PM 10 (PM 10 out), ventilation operation, shape and depth of platform.

In [START_REF] Delavar | A Novel Method for Improving Air Pollution Prediction Based on Machine Learning Approaches: A Case Study Applied to the Capital City of Tehran[END_REF], air pollution is forecasted using spatio-temporal data of city of Tehran, Iran obtained over a span of 10 years. Several machine learning methods such as; regression support vector machine, geographically weighted regression, artificial neural network and auto-regressive nonlinear neural network are evaluated on two datasets, one of which is cleaned via Savitzky-Golay filter while the other dataset was noisy due to missing entries. On both datasets, nonlinear autoregressive exogenous (NARX) neural network displays superior performance with exceptional performance over the former dataset.

Prediction Model Framework

In this article, we use a recurrent neural network that is; long short-term memory (LSTM), to capture the temporal trends of pollutant data. LSTM's perform better on sequential data as it takes the historical events into account by taking the output at instant t-1 as input in addition to inputs at t. This characteristic introduces the concept of Memory in neural networks which is of import when it comes to analyzing data of pollutants as it varies temporally.

Equation 1 and 2 describe the working of an RNN; where H is the tanh activation function, W defines the weight matrices between hidden and input layer (W xh ), hidden and hidden layer (W hh ), hidden and output layer (W hy ), x t the input sequence, h t the hidden vector of a module at instant t and b the bias to compute output y t by iterating across these equations from t=1 to T.

h t = H(W xh h xt + W hh h t-1 + b h ) (1)
y t = W hy h t + b y (2)
Though, RNN perform better when the sequences are short but suffer inherently from exploding gradient problem when working with data having long term dependencies. This problem is tackled by LSTM's which due do its gated memory architecture resolves the issue of vanishing and exploding gradients and is able to retain information for an extended period of time. Equation 3, 4, 5, 6 describes the input, forget and output gate and cell activation vectors of LSTM architecture respectively. Where σ is the sigma activation function.

i t = (W xi x t + W hi h t-1 + b i ) (3)
f t = (W xf x t + W hf h t-1 + b f ) (4)
o t = (W xo x t + W ho h t-1 + b o ) (5)
c t = f t * c t-1 + i t * tanh(W xg x t + b g ) (6)
h t = o t * tanh(c t ) (7)

Employed Datasets

The architecture was evaluated using two datasets, the modified UCI dataset published by [START_REF] Reddy | Deep Air: Forecasting Air Pollution in Beijing, China[END_REF] and on a dataset we introduced with parameters recorded in Lahore, Pakistan. The modified UCI dataset has meteorological data of wind speed, direction, air pressure, temperature, dew point, wind speed, cumulative rain hours and cumulative snow hours. Pollutant data of only PM 2.5 is recorded 25 times throughout the day. The parameters are collected over a span of 7 years with 43,825 samples from 2010 to 2017 across 35 different stations in Beijing, China. We have taken average of the data per day and on the basis of PM 2.5 concentration, we calculate the AQI value which is determined by the standard formula developed by environment protection agency (EPA), US. Based on the AQI value, a column of hazard level is added to the dataset. The information of date, hour, day, month, and year in the dataset is removed and pre-processed using normalization. We obtained the time series pollutants data from environmental protection agency (EPA) Panjab, Pakistan for a span of 2 years from 2017 to 2019. The data of air pollutants is received from 6 stations across the city which includes particulate matter (PM 10 , PM 2.5 ), Nitrogen dioxide, Sulphur dioxide and surface ozone. The meteorological parameters play an instrumental role towards pollution dissemination and concentration in a particular region, thus the meteorological department of Pakistan was contacted to obtain the statistics of wind direction, temperature, barometric pressure, humidity, visibility and type of weather. The data of air pollutants and meteorological statistics are combined and pre-processed to form a dataset of 1500 samples for monitoring and predicting the hazard levels in the form of AQI. We have categorized the hazard into six levels according to the pollutants concentration defined by air quality index (AQI) values set by EPA, US as described in figure 1.

Fig. 1: Air Quality Index set by environment protection agency, US

Network Architecture

The frame work comprises of three layers; a single LSTM layer followed by two dense layers with activations of Tanh and softmax respectively.

The network is evaluated on Lahore dataset by using metrics of sparse categorical cross entropy and accuracy. Batch size of 16 is used with adam as an optimizer and the network is trained for 300 epochs with a data split of 70/15/15 for training, validation and testing. For modified UCI dataset, the network is trained for 300 epochs with a data split of 70/15/15, batch size of 8 and adamax as an optimizer. Python packages of Keras, tensorflow, Scikit-Learn and Pandas are used to model the network. Early stopping techniques are used by observing the loss on the validation data to reduce over-fitting by curtailing the training period.

Tuning Network Hyper-parameters

The hyper-parameters of LSTM model is then tuned based on data to configure optimal parameters. Batch size, Numbers of training epochs, optimizer, learning rate and type of activation function are some of the hyper-parameters tuned by employing grid search algorithm (GSA) to improve performance of the model. We started with tuning the number of training iterations and batch size simultaneously. The model was modified based on these optimal hyper-parameters and the grid search algorithm was run again to find an appropriate optimizer. The model was then tuned based on these parameters to find an activation function that boosts the performance of the LSTM model using grid search algorithm. According to the results of grid search algorithm, for Lahore dataset, the optimal hyper-parameters for the LSTM model are listed in table 1,2, 3 and 4. In 2, we select tanh as an activation as it gives better performance with all the other parameters tuned. The optimized hyper-parameters highlighted in italics are reconfigured by incorporating early stopping criterion using the validation set which improves the performance of the model employed.

Result and Analysis

The hyper-parameters are tuned using grid search algorithm on the training set and on the validation data with respect to the categorical cross entropy error. It is observed that the model performs best with batch size of 8 with training of 300 epochs on the Beijing dataset and batch size of 16 with training of 300 epochs on Lahore dataset. Moreover, adam and adamax are employed as an optimizers for Lahore and Beijing datsets respectively which helps in convergence at a faster pace. Figure 2 shows that model when trained for 300 epochs on the modified UCI dataset attains a maximum validation accuracy of 98.9583% at epoch 288 and an accuracy of 98.95% on the test set. Thus the temporal characteristic of the data is modeled quite accurately using the recurrent network architecture. Figure 3 depicts the prediction model performance on the test set.

The second dataset comprises of parameters recorded over a span of 2 years, thus after tuning the hyper-parameters, we train the network with a batch size

Conclusion

A model for forecasting hazard level has been devised and its performance is evaluated on the meteorological and pollutant data of two of the most polluted cities in the world; Beijing, China and Lahore, Pakistan. It is observed that despite different topography and meteorological information, the proposed network models the complexity of the diverse temporal information quite well. The proposed architecture after employing GSA optimization is able to forecast the hazard levels of the next 24 hours with an accuracy of 95.0% on the data recorded in Lahore, Pakistan and 98.95% on Beijing, China dataset due to ability of LSTM's to model temporal data and is thus able to learn the trends of air pollutants. This is an effective measure for the people going out to take necessary precautions and assist the environment protection agencies to enact policies and take steps towards reducing the health and economic risk caused due to high level of pollutants.

Acknowledgment

We would like to thank NCAI for funding this study. The modified UCI dataset employed in our study have been acquired from [START_REF] Reddy | Deep Air: Forecasting Air Pollution in Beijing, China[END_REF]. The second dataset was created by the data of pollutants taken from EPA lahore, Pakistan and meteorological parameters from Pakistan meteorological department.

Fig. 2 :Fig. 3 :

 23 Fig. 2: Network training results on modified UCI dataset

( a )Fig. 4 :Fig. 5 :

 a45 Fig. 4: Network training results on Lahore, Pakistan dataset

Table 1 :

 1 Selection of training iterations and Batch size using GSA on Lahore dataset

	Batch Size Epoch Number Accuracy
	16	300	0.92832
	8	350	0.92115
	16	350	0.91398
	8	300	0.91398
	32	350	0.91039
	32	300	0.91039
	64	350	0.89964

Table 2 :

 2 Optimal activation function selection using GSA on Lahore dataset

	Activation Function Accuracy
	softsign	0.92832
	tanh	0.92473
	hard sigmoid	0.92115
	linear	0.92115
	relu	0.91039
	softplus	0.91039
	sigmoid	0.90323
	softmax	0.82079

Table 3 :

 3 Results Of optimizer selection using GSA on Lahore dataset

	Optimizer Accuracy
	Adam	0.931899
	Adadelta	0.92473
	Nadam	0.91756
	Adamax	0.91398
	RMSprop 0.91039
	Adagrad	0.88889
	SGD	0.55197

Table 4 :

 4 Optimal learning rate selection using GSA on Lahore dataset

	Learning Rate Accuracy
	0.002	0.935454
	0.001	0.921169
	0.01	0.914026
	0.2	0.896169
	0.1	0.889026
	0.3	0.462922

Table 5 :

 5 Selection of training iterations and Batch size using GSA on modified UCI dataset

		Table 6: Optimal activation function
		selection using GSA on modified UCI
		dataset
	Batch Size Epoch Number Accuracy 8 300 0.98609 32 300 0.98609 64 500 0.98510 16 300 0.98411 64 300 0.98361 32 500 0.98312 16 500 0.98262 8 500 0.98213 8 100 0.97120	Activation Function Accuracy tanh 0.98709 hard sigmoid 0.98560 sigmoid 0.98560 linear 0.98312 relu 0.98262 softsign 0.98262 softplus 0.98064 softmax 0.87388
	Table 7: Results Of optimizer se-lection using GSA on modified UCI dataset	Table 8: Optimal learning rate se-lection using GSA on modified UCI dataset
	Optimizer Accuracy Adamax 0.98759 Adadelta 0.98461 RMSprop 0.97617 Adam 0.97567 Nadam 0.97368 Adagrad 0.95680 SGD 0.94836		Learning Rate Accuracy 0.002 0.972691 0.001 0.951837 0.01 0.943893 0.1 0.936941 0.2 0.935452 0.3 0.767130


Nadia Masood Khan
email: nadia.m.khan@durham.ac.uk

Gul Muhammad Khan

Peter Matthews
email: p.c.matthews]@durham.ac.uk

AI based Real-Time Signal Reconstruction for Wind farm with SCADA Sensor Failure

Keywords: Signal reconstruction, SCADA data, condition monitoring, linear regression, random forest, and neural network

Supervisory Control and Data Acquisition (SCADA) systems used in wind turbines for monitoring the health and performance of a wind farm can suffer from data loss due to sensor failure, transmission link breakdown or network congestion. Sensory data is used for important control decisions and such data loss can make the failures harder to detect. This work proposes various solutions to reconstruct the lost information of important SCADA parameters using Linear and nonlinear Artificial Intelligence (AI) algorithms. It comprises of three major contributions; (1) signal reconstruction from other available SCADA parameters, (2) comparison of linear and non-linear AI models, and (3) generalization of the AI algorithms between turbines. Experimental results demonstrate the effectiveness of the developed methodologies for reconstruction of the lost information for valuable planning decisions.

Introduction

Wind energy generation is an ideal source of green energy due to which the capacity of wind farms has been increased 30 times with a 17% cumulative growth in the last few years. Wind energy is expected to supply 12% of worldwide energy demand by 2020 [START_REF] Wan | Direct quantile regression for nonparametric probabilistic forecasting of wind power generation[END_REF]. Due to growth in the wind industry, wind turbines are most likely to be installed in diverse climatic conditions, onshore and offshore which would need continuous monitoring. These systems are monitored using a Supervisory Control and Data Acquisition (SCADA) system for their operation and performance. Unexpected failures of wind turbine components cause an increase in machine downtime, repair cost and subsequently cost of energy. Condition monitoring is often used to monitor health parameters, e.g. temperature or vibration that shows the condition of a machinery and any significant change in its pattern is indicative of developing failure [START_REF] Da Silva | Fault diagnosis in rotating machine using full spectrum of vibration and fuzzy logic[END_REF]. One of the most significant problems arises when a communication link or a sensor fails causing faulty or no data to be received for timely probable control decisions [START_REF] Marti-Puig | Different approaches to scada data completion in water networks[END_REF]. This research develops a system for reconstruction of the lost signal from low correlated parameters when one of the SCADA sensors fails to send data. Linear and non-linear AI algorithms have been analysed to find a generalized model which will be robust and perform better for all wind turbines in a wind farm rather than one turbine. The wind power curve defines the relationship between wind speed and power. It is frequently used to monitor the health of a wind turbine using SCADA data received from other system parameters. This study will assume that wind power, being the most important parameter to monitor the performance and health of a wind turbine, is lost or corrupted in transmission. Artificial intelligence (AI) based models are extensively used in detecting failures and predicting wind power from a SCADA system of a wind farm [START_REF] Qian | A novel condition monitoring method of wind turbines based on long short-term memory neural network[END_REF].

Research in the literature is focused mostly on signal reconstruction from historical data. Signal reconstruction from other available parameters was never considered as an option. The motivation of this research is to reconstruct a signal when one of the SCADA sensors fails to send data either due to a sensor failure or a communication breakdown for longer than expected. Also, when the highly correlated variables and historical data is not available for a very long time, signal reconstruction becomes vital for optimum operation of the plant. Electrical power generated from a wind turbine is considered to be the corrupted/lost signal in this case, since it is the most important parameter describing the normal operation of a wind turbine and is hard to predict due to its high degree of fluctuations and randomness. AI algorithms have the ability to learn and model the non-stationary behaviours. We have explored two AI methods: random forest and Cartesian Genetic programming evolved Artificial Neural Network (CGPANN) and then compared these results with a linear regression model to find out the best performing model for accurate estimation of the failed sensor data. Training and test results on the same turbine demonstrate random forest performing much better than its counterparts. Its performance degrades when tested on data from other wind turbines in the same wind farm. The CGPANN model having multilayered feed-forward architecture arranged in Cartesian format show remarkable generalization and continue to perform better in diverse data conditions [START_REF] Hassanzadeh | Transferability of artificial neural networks for clinical document classification across hospitals: A case study on abnormality detection from radiology reports[END_REF].

Background

SCADA collects data from a machine and send it to a central processing unit for proactive measures. Data collected and stored from SCADA comprises of information regarding every aspect of a wind farm which can be used to infer overall health of the wind turbine in real-time. SCADA systems are often at risk due to various factors such as the sensor failure or network congestion, limited power or equipment abnormality resulting in data loss [START_REF] Liu | A statistical learning framework for the intelligent imputation of offshore wind farm missing scada data[END_REF]. Sensor failure means it might be sending abnormal data or not sending data at all, this work is focused on the latter one. Missing/lost data is a challenge faced in engineering and industry specifically in applications employing sensing technologies implementing intelligent real-time monitoring and control such as an offshore wind farm SCADA data and wireless sensor networks [START_REF] Liu | A statistical learning framework for the intelligent imputation of offshore wind farm missing scada data[END_REF]. A framework for the effective data management and dealing with issues of missing and corrupted samples in the acquired data is developed in [START_REF] Martinez-Luengo | Data management for structural integrity assessment of offshore wind turbine support structures: data cleansing and missing data imputation[END_REF] for effective fatigue assessment of offshore wind turbines. Yang et al. [START_REF] Yang | Real-time condition monitoring and fault detection of components based on machine-learning reconstruction model[END_REF] proposed a machine learning based reconstruction model for real-time condition monitoring and fault detection. They performed correlation analysis to select input parameters and then used Support Vector Regression (SVR) for building a reconstruction model. Their focus was on failures caused due to high temperature, so signals relevant to temperature faults are selected as input features to estimate generator drive end temperature. Singh [START_REF] Singh | Analytical techniques of scada data to assess operational wind turbine performance[END_REF] used wind power curve to identify the abnormal operation of a wind turbine. Wind power being considered the vulnerable parameter, since deviation of power from its normal operational values helps in identifying probable failures in advance. Establishing a generalised model to reconstruct the lost/corrupted SCADA signal of wind power is the focus of this work. Lind et al. [START_REF] Lind | Normal behaviour models for wind turbine vibrations: Comparison of neural networks and a stochastic approach[END_REF] have explored a stochastic approach to reconstruct the tower top acceleration signals from a single external variable, i.e. wind speed and previous values of the tower top acceleration. Their finding was that signal reconstruction can be used to monitor and detect abnormal behaviour. De-noising auto-encoder (DAE) is proposed in [START_REF] Ahmed | Mitigating the impacts of covert cyber attacks in smart grids via reconstruction of measurement data utilizing deep denoising autoencoders[END_REF] for reconstruction of original sensor measurements from a corrupted SCADA system due to covert cyber-deception attack (CCDA). An ad-hoc method is presented in [START_REF] Marti-Puig | Double tensor-decomposition for scada data completion in water networks[END_REF] to reconstruct the long bursts of data lost by SCADA due to sensor or communication failure. Lamrini et al. [START_REF] Lamrini | Data validation and missing data reconstruction using self-organizing map for water treatment[END_REF] applied self-organizing map (SOM)-based methods for the reconstruction of data from a water treatment system to deal with data loss due to sensor failure or corrupted input data. A number of statistical and artificial intelligence models have been proposed for wind power estimation to prevent damage to wind turbines and ensure stability of the power system. Sun et al. [START_REF] Sun | Multistep wind speed and wind power prediction based on a predictive deep belief network and an optimized random forest[END_REF] proposed a hybrid model of deep belief networks (DBN) and random forest for short term wind power forecasting.

Dataset

SCADA is widely used in different areas for monitoring and control in real time. The SCADA data used in this study is acquired from La Haute Borne wind farm (ENGIE Green) 3 which consists of four wind turbines from Senvion MM82 technology located in the Grand East region in north-eastern France. The SCADA system collected data from 31 parameters along with their statistics such as average, maximum, minimum and standard deviation of each parameter. Since the average value of these parameters captures most of the information, only the average value of each parameter has been used for the experiments. Each data point is sampled at 10 minute interval. Nominal power for each turbine at the La Haute Borne wind farm is 2050 kW, with a rotor diameter of 82 m and a hub height of 80 m. Cut in wind speed of 3.5 m/s, nominal wind speed of 14.5 m/s and cut-out wind speed of 25 m/s. Some of the parameters from the dataset are, active power, reactive power, vane position, wind speed, nacelle angle, gearbox bearing temperature, generator bearing temperature, pitch angle, torque and converter torque. The layout of the wind farm with latitude/longitude and inter-turbine distances in meters is shown in Figure 1. The wind farm comprises of four wind turbines: R80711, R80780, R80721 and R80736.

Methodology

The objective of this work is to develop a reliable signal reconstruction model for wind power prediction from other SCADA parameters. This is necessary because the power produced from a wind turbine depicts its health statistics and eventually help in monitoring the condition of a wind turbine. Accurate wind power prediction has a significant economical and technical impact for a reliable large-scale wind power integration and important energy management planning decisions. There has been ample work carried out to estimate power generated from wind speed and an acceptable accuracy is reported in literature [START_REF] Barbosa De Alencar | Different models for forecasting wind power generation: Case study[END_REF]. The challenging part is to estimate wind power when the closely correlated parameters such as wind speed, torque, apparent power, rotor speed etc. are not available, and the system has to predict highly fluctuating wind power from very low correlated parameters with non-linear and non-stationary characteristics. This work is focused on restoring the lost information from the low correlated parameters, assuming that all the highly correlated parameters are missing. Due to the non-linear nature of the problem, an adequately accurate algorithm needs to be developed to model this complex relationship. Wind power is estimated in absence of highly correlated variables. Any deviation of a power curve from its normal operational values is indicative of a number of faults such as blade pitch angle failure, blade damage, pitch control failure and blades affected by ice or dirt [START_REF] Stetco | Machine learning methods for wind turbine condition monitoring: A review[END_REF].

The idea is to develop a model in which the output has low correlation with input signals and input signals have low cross-correlation with one another [START_REF] Schlechtingen | Comparative analysis of neural network and regression based condition monitoring approaches for wind turbine fault detection[END_REF]. As part of the methodology, a correlation matrix has been generated and input signals having an absolute cross-correlation coefficient greater than 0.8 are removed from input when developing wind power signal reconstruction model in this study. One year (2014) data is divided into 3 segments based on wind speed. Figure 2 shows the performance curve for each region. The first segment contains the data when the wind speed is below cut-in and the turbine blades are trying to overcome friction. There is no power produced in this region. Instead the wind turbine takes power from grid to keep the turbine blades moving to prevent damage to blades due to ice and dust. The second segment is the most important to model, as it contains data above cut-in speed to rated wind speed; there is a rapid growth in power produced. In segment 3, constant power is produced until the wind speed reaches the cut-off speed and the turbine is turned off to prevent damage due to excessive wind speed. These three segments represent the various key modes of wind turbine operation. Linear regression, random forest and CGPANN are implemented on each of the data segment and then on the data without segmentation. The data from wind turbine R80721 between 01/01/2014 to 31/12/2014 is selected for training and testing following the split strategy 75% training, 25% testing [START_REF] Kusiak | Short-horizon prediction of wind power: A data-driven approach[END_REF]. Testing has been performed on the same turbine and on data from the other three wind turbines in the wind farm. The reconstruction algorithm performance is tested on all three segments as well as on the whole dataset. Similarly, data from the other three wind turbines is divided into segments and evaluated to find the best signal reconstruction algorithm.

Multiple Linear Regression (MLR)

Linear regression is a statistical method used for prediction of a dependent variable from a single independent variable. It is termed as Multiple linear regression (MLR) [START_REF] Freedman | Statistical models: theory and practice[END_REF] when the dependent variable Y is predicted from a set of independent variables X k where k is an index of the predictor variables.

Y = β 0 + β 1 X 1 + . . . . + β k X k + (1)
The model parameters β 0 (intercept), β 1 to β k (regression coefficients) are learned from the data and is the residual standard deviation in Y. Python's Scikit-learn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF] has implemented a number of algorithms. The linear regression is implemented using the Scikit-learn library in this study on the transformed dataset.

Random Forest (RF)

Random forest [START_REF] Breiman | Random forests[END_REF] is a supervised machine learning algorithm which consists of an ensemble of decision trees. More trees means more robust performance. The ensemble decision trees are trained using a bagging method. This trains a number of learning models and its combination increases the overall results. RF can be represented as an ensemble of C number of trees T 1 (X), T 2 (X), ..., T C (X) having m inputs given by X = x 1 , x 2 , ...x m . The resulting ensemble produces C outputs Ŷ1 = T 1 (X), Ŷ2 = T 2 (X), ......, ŶC = T C (X) and the mean is calculated from the output of these randomly generated trees to give final prediction Ŷ of random forest regression tree.

Random forest comes under the umbrella of artificial intelligence models which develops decision trees with the root node having the most important feature. Random forest is implemented using Scikit-learn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF] and is used with the default parameter setting. Hyper-parameters are not optimized since it performed well with default parameters.

Cartesian Genetic Programming evolved Artificial Neural Network

Cartesian genetic programming evolved Artificial Neural Network (CGPANN) was first proposed in 2010 [START_REF] Khan | Evolution of neural networks using cartesian genetic programming[END_REF]. The study conducted in [START_REF] Khan | Breaking the stereotypical dogma of artificial neural networks with cartesian genetic programming[END_REF] shows that CGPANN has performed best when compared with Hidden Markov model (HMM), Auto

Regressive Integrated Moving Average (ARIMA), regression model, Classification and Regression tree (CART), and neural network model for time series prediction. The essence of CGPANN is to tune the hyper parameters using evolutionary programming called Cartesian genetic programming (CGP) instead of traditional gradient based methods. All neurons are arranged in Cartesian format in CGPANN. Recently, a single row format has been used, since it provides more flexibility of generating infinite graphs as shown in Figure 3. Figure 3 shows the CGPANN phenotype with corresponding genotype in part A and B. Not all neurons are connected in CGPANN while creating graphs from output to inputs. This ability of CGPANN provides the flexibility of generating arbitrary graphs. The numbers in genotype can change during evolutionary training using mutation operator, causing the network topology to change accordingly producing novel solutions to the problem. Direct encoding scheme is used to encode connection weights, connection type, and the topology of the network. The 1 + λ(λ = 9) evolutionary strategy is followed to produce population of probable solutions. In this work, the log sigmoid function is used as the activation function as represented by equation 3.

h θ (x) = 1 1 + e -θ T x (2)

Evaluation of Model Performance

The following two performance metrics are applied to evaluate the abilities of three models to reconstruct the wind power from loosely correlated parameters.

RootM eanSquareError(RM SE)

= ( 1 N ) n i=1 (y i -ŷi ) 2 (3) M eanAbsoluteError(M AE) = 1 N n i=1 |y i -ŷi |. ( 4
)
where y i is the actual value, ŷi is the estimated value and N is the total number of observations.

Experimental Setup

The proposed wind power reconstruction model is trained on the parameters available in the SCADA dataset under consideration. The framework for the experimental setup is shown in Figure 4. Conditioning monitoring data from the SCADA system is segmented based on different wind speeds, it results in four sub-dataset. Each segment is analysed separately to select inputs for training. Figure 5 shows the correlation heat map for each segment. The heat map is used for two purposes in this research, first to verify the different modes of operation of a wind turbine by showing the difference in heat map of each segment. It demonstrates that correlation between different variables varies across various segments. Second, to locate the variables having an absoulute cross-correlation greater than 0.8 and removing these from the input. The main aim of this research is to reconstruct the important parameter i.e. wind power which shows the health of a wind turbine from poorly correlated input parameters. Pitch angle Ba has very low correlation with power in segment 1, but noticeable negative correlation in segment 2 and 3. Blade pitch angle keeps on changing to capture most of the wind energy. When the power production gets low due to change in wind direction in segment 2, pitch angle is changed to increase the power production. In segment 3, when power reaches its rated maximum value, pitch angle is adjusted to stop production and prevent turbine blades from damage. Similarly, wind speed is recorded by three sensors (Ws, Ws1, Ws2) at different locations in a wind turbine. Wind speed has highest correlation with power in segment 2, since power produced relies on wind speed in this region. In segments 1 and 3, correlation between wind speed and power produced is low as there is constant power produced due to wind energy in these two regions. The heat map demonstrates various operational modes in each segment to exploit wind turbine physics. After the input selection, each sub-dataset is split into training and testing data. Training data is then used to develop three reconstruction models using Linear Regression, Random Forest and CGPANN. The trained reconstruction models are then tested on two types of testing datasets, that include testing data from same wind turbine it is trained on and the data from other three wind turbines in the same wind farm.

Results and Analysis

To validate the performance of linear and non-linear methods for wind power reconstruction, experiments have been carried out on four wind turbines' data for the year 2014. Table 1 shows the results obtained by testing the trained algorithms' performance on different segments and all year (2014) data of the turbine R80721. Random forest (RF) performs exceptionally well in all three segments as well as on the overall data without segmentation when tested on same wind turbine data (R80721) it has been trained on. Random forest performs well on segments 1 and 2 giving mean absolute error (MAE) of 0.02. On segment 3 MAE is 0.06 and on data without segmentation MAE is 0.05. High values of error on complete data shows that the data segmentation can be helpful in accurately reconstructing the power production of a wind turbine from other SCADA parameters. Trained models have been evaluated for their performance on other wind turbines from the same wind farm to check if the developed models had learned the power variation and fluctuation pattern in wind farms in general rather then learned a single wind turbine's operation. Table 2 shows the performance of the three trained reconstruction models on different wind turbines in the same wind farm. Random forest (RF) still performs well in segment 1 due to the fact that segment 1 does not have a lot of variations and power produced in this region is constant. Ideally, the wind turbine does not produce any power below cut in wind speed, but it is not the case in real time as the wind turbine takes power from national grid to keep the blades rotating slowly in the cold weather to prevent icing. Overall, it should be noted that CGPANN outperforms random forest and linear regression in all three wind turbines. Segment 2 is the most important operational region of all as it has a lot of variations in power produced based on different wind speeds. The relationship between wind power and other SCADA parameters is not linear in this region which can be seen in Table 2 that linear regression has highest error in segment 2. While CGPANN has lowest MAE of approximately 0.14 and the random forest having MAE ≈ 0.6 which verifies that a neural network has the property of transferability and able to learn the power patterns in a wind farm. In Table 2, the low error on all data without segmentation when tested on different wind turbines is because segments 1 and 3 have low errors as compared to segment 2. Table 3 depicts the size of data in each segment. This emphasizes the importance of segmentation as the model might show good performance on all data but not well on segment 2 with high variations as shown in Table 2.

Conclusion and Future Work

This paper presents a methodology to deal with the challenge of wind power estimation from low correlation data and proposes a signal reconstruction model for wind power in case of SCADA sensor failure in a wind farm. The proposed model can be used to monitor the wind power signal continuously even when the power sensor fails and the signals of parameters that are highly correlated with wind power are also not received either. Linear regression, random forest and CGP evolved ANN is used for real time prediction of electric power produced from a wind turbine. Data segmentation based on wind speeds help in the accurate estimation of wind power and emphasizes the importance of segment 2. Although Random Forest testing results are better for a specific wind turbine, CGPANN generalizes better when exposed to wind turbines other than it is trained on. Accurate and timely prediction of these important parameters are able to help in important decisions for a wind farm. This work can be extended to the cases where more than one sensor fails. In future, the reconstructed signal will be used to identify faults in the wind turbine so that an alarm can be generated before the actual failure.

Fig. 1 .

 1 Fig. 1. Wind Farm Layout.

Fig. 2 .

 2 Fig. 2. Typical Power Curve for a Wind Turbine.

Fig. 3 .

 3 Fig. 3. a. CGPANN Phenotype, b. CGPANN Genotype

Fig. 4 .

 4 Fig. 4. Framework of wind power data reconstruction model

Fig. 5 .

 5 Fig. 5. Heat map showing cross-correlation between input parameters in each segment.

Table 1 .

 1 Testing Results for Wind Turbine 80721

	Error	LR	RF CGPANN
	Segment 1 MAE 0.1321 0.0251 0.1020
	RMSE 0.0192 0.0071 0.0513
	Segment 2 MAE 0.0760 0.0274 0.1163
	RMSE 0.1004 0.0488 0.1838
	Segment 3 MAE 0.0961 0.0669 0.0092
	RMSE 0.0961 0.0681 0.0097
	All Data MAE 0.1043 0.0500 0.1135
	RMSE 0.1302 0.0851 0.1838

Table 2 .

 2 Performance evaluation in terms of MAE and RMSE for various turbines

			R80711	R80736	R80790
	Error	LR	RF CGPANN LR	RF CGPANN LR	RF CGPANN
	Segment 1 MAE 0.1321 0.0251 0.0209 0.3686 0.0562 0.1368 0.3064 0.0681 0.1020
	RMSE 0.1777 0.0563 0.0503 0.3842 0.0853 0.1417 0.3246 0.0834 0.1077
	Segment 2 MAE 2.2599 0.6258 0.1432 2.7365 0.6469 0.1455 2.6814 0.6462 0.1337
	RMSE 2.3981 0.6559 0.1980 2.8903 0.6737 0.2285 2.8701 0.6728 0.1951
	Segment 3 MAE 0.0900 0.1537 0.0197 0.0945 0.1909 0.0668 0.0689 0.2737 0.0193
	RMSE 0.0987 0.1797 0.0448 0.1131 0.2156 0.0754 0.0848 0.3037 0.0249
	All Data MAE 0.2391 0.1302 0.1313 0.2336 0.1292 0.1306 0.2317 0.1216 0.1220
	RMSE 0.3350 0.2100 0.1903 0.3277 0.2196 0.2116 0.3134 0.1762 0.1860

Table 3 .

 3 Wind turbines training and testing data size

		R80721		R80736
		Training Testing Testing
	Segment 1 7959	2654 10530
	Segment 2 39420 13140 40520
	Segment 3	8	3	22
	All Data

ENGIE Green, https://opendata-renewables.engie.com/explore/dataset/la-hauteborne-data-2013-2016/